WHY IS KADDISH SO IMPORTANT?

May as well start with the biggest one of all. 

if you can say "AMEN." You have learned the most essential part needed in being either a mourner, or part of a minyan as a comforter to the mourner.
 
 The Kaddish prayer itself is not in the Torah, and is actually not considered a biblical or rabbinic mitzvah.  Originally the Mourner’s Kaddish we say today was said at the end of a study session of Talmud.  The earliest sources of Kaddish becoming a mourner’s prayer date from the middle ages -- the early 12th century -- where it was said on behalf of orphaned children who had not yet reached bar mitzvah age but thereafter it became a widely held custom. The prayer is not Hebrew, but Aramaic, the chosen language spoken at the time (the word Kaddish is Aramaic for holy) and its recitation brings holiness to G-d's name and to all those who respond "Amen" while it is being recited.  The Kaddish is considered a very simple prayer that even the illiterate and unlearned of the day could recite so they could lead the prayer while mourning.  Originally meant for natural born, adoptive and stepsons to say for their parents, the practice has evolved, in modern Jewish settings, to including any family member, male or female.
 
Jews pray 3 times a day — morning, afternoon and evening. There are 8 opportunities in the 3 services each day to say Kaddish, but the Mourner's Kaddish is said only at the end of each service, and must be said with a congregational presence.
 
There are five forms of Kaddish:

1. Half (Chatzi) Kaddish: Recited during services to indicate the conclusion of minor sections of the prayer service.
2. Complete Kaddish (kaddish shalem),  Same as the half-Kaddish, but adds the section Titkabel ("May the prayers be accepted...") and concluding paragraphs. This is recited after the conclusion of major sections of the prayer services.
3. Kaddish-Yatom (the Mourner's Kaddish): This Kaddish is the same as the half-Kaddish, but adds the section rhey Shloma ("May there be abundant peace...") and concluding paragraphs. It is recited by mourners at specific points during the services.
4. Kaddish-D'Itchad'ta: Recited at the conclusion of a major tractate of Talmud, and at a funeral. Just as one who concludes a major tractate of the Talmud, which is a holy endeavor, recites Kaddish, so, too, one who passes from this world has completed a holy endeavor and thus, this Kaddish is recited.
5. Kaddish-D'Rabannan: This Kaddish is the same as the half-Kaddish, but adds the section Al Yisrael ("Upon Israel, upon our sages...") and concluding paragraphs. This is recited after the conclusion of studying a section from the Talmud or Mishna.

 The Jewish concept of mourning is not about death, it's about life.
 
In Judaism, death is not a tragedy, even when it occurs early in life or through unfortunate circumstances. Death is a natural process. Our deaths, like our lives, have meaning and are all part of G-d's plan. In addition, we have a firm belief in an afterlife, a world to come, where those who have lived a worthy life will be rewarded.

A distinct number of days is allotted in which a person is to mourn.

• The world was created with humanity as its focus. This took a full cycle of time: seven days. When creation is reversed and the human soul returns to its source, that, too, is marked with a week's cycle: the Shivah, seven days which the closest relatives devote exclusively to mourning the soul's departure, and the extended family, friends and community comfort them with their presence, their empathy, and their words of consolation.
• Shloshim -  30 days for the loss of a sibling, spouse, or child, but 11 months for a parent.  Why 11 months and not a full year? -- The deceased is considered to be under Divine judgment for that period, but a full year of 12 months is the duration of judgment for the wicked. Since we presume our parents do not fall into that category, Kaddish is said for them so that there are a full 30 days between the last recitation and the end of the Jewish calendar year. 
• After the required period of mourning, the mourner is obligated to rejoin the living and continue to honor the memory of their deceased with the Kaddish on the anniversary of their death (Yahrzeit) and also in their daily deeds.

The Kaddish prayer doesn't even mention death or focus on the past, but speaks of the future and a prayer for better days ahead and of peace. The repetition of the Kaddish through the period of mourning points to your own post-mourning future, to the belief that the sorrow will lift, that life will be renewed, and that the world, both heaven and earth, will someday be redeemed.
 
Although the context of saying a Mourner's prayer is a very private thing, there are certain prayers in Judaism expressing the adoration of G-d and must be prayed in the midst of a congregation of adult thinking men and women, which is the age of bar/bat mitzvah -- this is called a minyan.. But according to the Rabbis, even if a mourner needs someone else to lead the prayer, simply the act of responding Amen is the same thing as saying the entire prayer.
 
Because it became such a universal prayer among Jews in the diaspora, any traveler could become part of a minyan in any community and either continue their mourning for the loved one, or be part of a minyan and bring comfort to someone in mourning. So as a prayer, Kaddish, when said in a minyan, unites generations in a vertical chain — parent to child — while uniting Jews on a horizontal plane, bringing together neighbors.

SHABBAT & HAVDALLAH?

WHAT RITUALS ARE PERFORMED FOR SHABBAT, AND WHY?

According to halakha (Jewish religious law), Shabbat is observed from a few minutes before sunset on Friday evening until the appearance of three stars in the sky on Saturday night, at which time Shabbat is closed with a havdallah blessing.  Judaism accords Shabbat the status of a joyous holy day. In many ways, Jewish law gives Shabbat the status of being the most important holy day in the Jewish calendar:  The Tanakh and siddur describe Shabbat as having three purposes:

1.      To commemorate God's creation of the universe, on the seventh day of which God rested from (or ceased) his work;
2.      To commemorate the Israelites' redemption from slavery in ancient Egypt;
3.      As a "taste" of Olam Haba (the Messianic Age).

There are three (3) main components of ushering in the Sabbath -- candles, wine and challah. 

CANDLES -- At least two candles should be lit, representing the dual commandments to remember, and to observe the sabbath, but many families light more to represent the number of their children.  The prayer said over the candles is done by the female head of house, or by a man if he is single.  After lighting, she waves her hands three times over the candles, welcoming in the sabbath. Then she covers her eyes, so as not to see the candles before reciting the blessing, and recites the blessing below. The hands are then removed from the eyes, and she looks at the candles, completing the mitzvah of lighting the candles.

When Jews ushered in the Sabbath in biblical times, the likelihood is they used oil rather than candles.  Candles became a more accepted practice during the Diaspora, probably brought from Europe.

Blessing over Candles

Barukh atah Adonai, Eloheinu, melekh ha'olam Blessed are you, Lord, our God, sovereign of the universe

asher kidishanu b'mitz'votav v'tzivanu Who has sanctified us with His commandments and commanded us

l'had'lik neir shel Shabbat. (Amein) to light the lights of Shabbat. (Amen)

WINE -- Wine is a celebratory beverage, that serves to show that the meal we are about to eat isn’t just another regular meal, but a special, joyous and festive one.  The full prayer over the wine can be found here but the shortened versoni is also acceptable.

Barukh atah Adonai, Eloheinu, melekh ha-olam Blessed are you, Lord, our God, sovereign of the universe

(if using wine or grape juice) borei p'ri hagafen (Amein) Who creates the fruit of the vine (Amen)

CHALLAH -- Traditionally two loaves of challah are used, representing the dual portion of manna that God provided for the Israelites in preparation for Shabbat in the desert. The challah loaves should be whole, and covered.  But why must they be covered?  The sages determined that saying the blessing over the bread takes priority over the blessing for the wine except on Shabbat, when the blessing over the wine is said first.  To preserve the sanctity and respect for the bread and to not "shame" it for taking on secondary import, a cover is placed over top.  While challah covers can be very ornamental, a simple napkin or towel will also suffice.  Some families tear the challah and pass it around, and others cut it.  Tearing is more traditional, but either way is fine.

Barukh atah Adonai, Eloheinu, melekh ha-olam Blessed are You, Lord, our God, King of the Universe

hamotzi lechem min ha'aretz. (Amein). who brings forth bread from the earth. (Amen)

WHAT RITUALS ARE PERFORMED FOR HAVDALLAH, AND WHY?

The basic havdalah formula was composed by the Men of the Great Assembly at the time of the second temple in the fourth century BCE.  It is when we rehearse the divisions that separate the world of material reality from the world of spiritual reality. Shabbat is understood as a gateway to the supernal world and havdallah marks the transition in which the two worlds meet.  The ritual of Havdallah has three symbols:

WINE to represent the joy and sweetness of Shabbat, 

SPICES to comfort our Sabbath soul for the loss of Shabbat, On the seventh day [God] rested and was ensouled." This extra soul is within us just for Shabbat and departs from us when Shabbat ends. 

A BRAIDED CANDLE which represents the duality of the material and the spiritual worlds. While the blessing is made over the candle, there is a practice to gaze at one's cupped hand to observe the light of the candle off the fingertips and the shadow cast by the fingers on the palm. The contemplation of light and dark reminds us of the distinction between the world that we can see around us and the hidden world of God's presence; the reflected light off the fingernails further symbolizes that we are beings of light.

Blessings are made over each symbol, followed by a blessing to sanctify the distinction between Shabbat and the rest of the week. Then the candle is extinguished in the wine and a new week is declared.

This is the Havdallah service we use at our get togethers.