Guten Tag RexV!
Let's dive right into your questions:
1. For the difference between geben and schenken, check out Lesson 5.7 in Level 1, Module 5. This lesson is all about the differences between these two verbs, and so you should find your answer there!
2. There is no such form as "zu kurzs," but perhaps this is a typo and you meant zu kurze? In any case, zu kurz may be using the undeclined form of the adjective kurz. You will see this used after the verb "to be" - for example, Die Geschichte war zu kurz "The story was too short." You will see the adjective kurz with other endings when it comes in front of the noun it describes and its ending must change to agree with the case and gender of the noun it is describing - for example, eine zu kurze Geschichte - literally "a too-short story." For a review on how adjective endings change, see Level 2, Module 10, Lesson 10.8.
Zu kurz can also be used as an adverb - for example, Es hat zu kurz gedauert "It took too short a time." In these situations, its ending will never change.
3. If in zu lang and zu lange, lang "long" is acting as an adjective to describe a noun, then the difference between these two forms will be the same as the difference between zu kurz and zu kurze explained above .
If lang is being used as an adverb (to describe an adjective, verb or other adverb), then you may see it as either zu lang or zu lange - there is no real difference between these two forms. The shorter version, zu lang, may indeed simply be what zu lange has changed into over time, as people have begun to speak more quickly and have let the e on the end drop. Zu lange, being the longer form, may put more emphasis on how long the thing being described was, and you may think of zu lang as being a more colloquial and less formal form; in general, though, you can use them interchangeably.
4. Level 1, Module 5, Lesson 5.8 goes through the verb machen and its present conjugations. As for when you should use machen in phrases like Wir machen ein Party (careful of your capitalization there), you will pick this up over time as you learn more and more German phrases.
5. The words nötig and notwendig are essentially interchangeable and both mean "necessary." You may notice some common phrases where one is normally used instead of the other, but these are the sorts of things that you will get used to over time as you learn more German.
6. Meins translates to "mine" and is a neuter form of the possessive pronoun. You can use it after "to be" in a sentence where the subject is not specified - for example, Das ist meins! "That is mine!" - or where the subject is neuter - for example, Das Kleid ist meins "The dress is mine."
I hope that these have answered all of your questions!