Because I am quite sure there is a way to say "I would like" in Portuguese, and I bet we will learn it before the end of the course. And also because they are not exactly the same. They are not on the same level of formality or politeness. And the verbs are in different tenses.
Yes. See my answer to EnhancedNightmare or some other reference like: http://www.elearnenglishlanguage.com/blog/english-mistakes/i-vs-me/
In isolation both of those are fine. As "you" can be both a subject and an object it can combine with either "I" (subject) or "me" (object), whereas previously "he" (subject) and "me" (object) clashed when combined.
You still need to choose the right combination in a sentence, though; it's not a simple case of using one in the USA and the other in the UK. Basically "You and I" is equivalent to "we" and "You and me" is equivalent to "us". For example, "You and I always argue" (think "we") is correct, but "You and me always argue" (think "us") is not. I'm not saying you'll never hear anyone say that, in fact, I'm sure you will, but it's non-standard.