Vayikra

1. Our dining room tables correspond to the מזבח/Altar (Br 55a, Mn 97a and Avos 3:3.) Besides the many mitzvos we do at our tables, in what specific way do we correlate the bread that we eat there with the offerings that are consumed by fire on the Mizbei'ach.
Salt 2:13.  SA OC 167:5, Rema:

 מצוה להביא על כל שלחן מלח קודם שיבצוע כי השלחן דומה למזבח והאכיל' לקרבן ונא' על כל קרבנך תקריב מלח (ב"י בשם שבולי הלקט) והוא מגין מן הפורענות (תו' והגהת אשיר"י פ' כיצד מברכין וע"ל ס"ס ק"ע):

2. Although our tables correspond to the Mizbei'ach, we are allowed to eat two things which we are never allowed to burn on the Mizbei'ach. Except one of them, for one week each year.
Chametz and honey, 2:11, 'כי כל שאר וכל דבש לא תקטירו ממנו אשה לה. Rav Hirsch has an interesting approach - this reminds us that luxuries may be enjoyed but should never be aspired to.

3. Identify the word, a homophone, that in our Parsha means ash but in other places means fat or luxury.
Deshen.  Here, 1:16, אל מקום הדשן, and in Mei'ein Sheva Friday night, ומניח בקדושה לעם מדושני עונג זכר למעשה בראשית.   See Tehillim 63:6,  כמו חלב ודשן תשבע נפשי ושפתי רננות יהלל פי, and Vayeilech, Devarim 31:20, כי אביאנו אל האדמה אשר נשבעתי לאבתיו זבת חלב ודבש ואכל ושבע ודשן. Harav Avraham Isenberg says they are related because ash is used to fertilize land, just as manure is called a "fertilizer."

4. Where in this Parsha is meat is referred to as "lechem" and matza as "Challah."
Eimurim, at 3:16, ואת שתי הכלית ואת־החלב אשר עלהן אשר על־הכסלים ואת־היתרת על־הכבד על־הכלית יסירנה והקטירם הכהן המזבחה לחם אשה לריח ניחח. Matza, the Menachos at 2:4, וכי תקרב קרבן מנחה מאפה תנור סלת חלות מצת בלולת בשמן ורקיקי מצות משחים בשמן. On a side, note, the ibn Ezra brings an opinion that because they are called Challos, these matzos need to be round, not square - ויש אומרים עגולות מלשון חלילה בדברי קדמונינו.

5.  In 1:17 Rashi says (from Mn 110) that the expression 'ריח ניחוח לה,  a pleasing fragrance, is found by a זבח/animal sacrifice and by a מנחה, which is a few pounds of flour and two cups of oil, to show that it doesn't matter if you spend a lot or a little. All that matters is what is in your heart, that you did your best.

אחד המרבה ואחד הממעיט ובלבד שיכוין לבו לשמים  

In Gemara parlance, the term for "expansive" is גם, gimmel mem, and the term for "limited" is אך, aleph chaph; (אֶתִים וְגַמִים ריבויין. אַכִין ְוְרַקִין מיעוטין) How are these two words directly related to the לב, the heart?
From the Ben Ish Chai:  Heart is leiv, lamed beis. The letters that precede gimmel and mem are beis and lamed. The letters that follow aleph and chaph are beis and lamed. When it comes to בין אדם למקום, there is no difference between them. All that matters is that they are from the heart.

Vayakhel and Pekudei

1. The brass altar in the courtyard is described as being "five amos long and five amos wide, square." The golden altar in the Heichal is "one ama long and one ama wide, square." The description "square" appears to be unnecessary. If all sides are equal, it's a square. What would we think if it wasn't described as being square? This pertains to practical halacha, because we have an oral tradition from Sinai that our Tefillin must be square, similar to the altars.
"Square" teaches geometric perfection of 90 degree corners and straight lines, so if it is a rhombus, or or there is a nick on the edge, it would be passul. The Meshech Chochma and Netziv in Ki Sisa 27:1  say additional answers regarding where the ribu'a has to begin and the application to the Mizbei'ach in the Mikdash which had different dimensions.

2.  If something has been used personally, can it be donated and used in the Mishkan?
From the Mar'os HaTzovos and the jewelry, yes, but only if it undergoes a significant physical change. See Magen Avraham OC 147 sk 5, אם שינה צורתן. But see Rav Hirsch here regarding the Kiyor.

3. What words in our parsha indicate that a mental resolution to give charity cannot be retracted and creates a legal obligation, and why do you think this applies uniquely to hekdesh/tzedakah.

Nediv Lev.  יו”ד סימן רנח, סעיף יג. Why? You’re on your own.

4. On the basis of a close similarity of its name, some scholars believe that one of the ingredients of the Anointing Oil was Cannabis. Which ingredient do you think that was?
Kenei Bosem. I'm not making this up. There are convincing reasons to believe this is the case.

5. If one only has enough for one candle, the Shabbos candle takes precedence over any other, including Chanuka. This is because of the vital importance of Shalom Bayis. On other days of the week, Chanuka takes precedence over Shalom Bayis. Apparently, avoiding friction on Shabbos is of greater importance than at any other time of the week. What passuk indicates that this is so.לא תבערו אש בכל מושבותיכם ביום השבת
See Gittin 52b about the Sattan instigating fights between a married couple every erev Shabbos and Reb Meir's intevention. 
See Shla'h Shabbos Ner Mitzva 32, where he says

 ועל כן עבירה כפולה היא מי שמראה כעס בשבת וכבר נתנו סימנים לא תבערו אש בכל מושבותיכם ביום השבת והוא אש המחלוקת וחימום הכעס 

and Chasam Sofer there in Gittin and Shaarei Ora I Ki Sisa.

6.  Moshe and Betzalel were required to give a precise accounting. For every penny they were given, they had to say "This is what I used it for." This was a public accounting given to Klal Yisrael, and it was presented in a fashion that the Jews all said "Well done. You used it all just as it ought to have been used."  After 120 years, when you come to the Olam Ha'Emes, you're going to undergo a Din v'Cheshbon. This Din v'Cheshbon will be like the cheshbon of Moshe and Betzalel in Parshas Pekudei. You are going to be asked, "You were given the ability to walk, to talk, to see, to feel, to think, to influence others, you were given intellectual and emotional gifts above others. What did you do with these precious gifts? You are now going to tell us exactly how you used your gifts, how you spent your time and money." It's not enough to convince yourself that you did the right thing. You're going to have to show the court that you did the right thing, Rochel Bitcha Haketana. Each one of us was given a Tafkid. How do you think you're going to do when you leyn your personal Parshas Pekudei?