The lessons skip around a bit, but Gostar means "to like" and if you are targeting a noun, like "I like water" you have to add "de", so you get "Eu gosto de agua".

It's like in "be afraid of" in english DE means that OF "Eu gosto de você" it means literally "I like of you". another exemple is "Eu tenho medo de cachorros" which means "I'm afraid OF dog" the difference is that in portuguese many verbs which are linked with the noun will need the particle DE. or Em like "Eu bato EM você" "I hit you"

The verb gostar requires an indirect object.

Because "de" is always after the verb "gostar", it's the way it's always. We have only to remember "gostar de"... instead of "gostar" alone.

yeah, well... thats kinda hard to explain... In portuguese you can't just say "they like you" that would be like "elas/eles gostam você". you have to connect the word or it won't have any sense... do you get?

Yes, in some varieties of Brazilian Portuguese —including those of Rio and São Paulo and most of Southern Brazil— this is the pronunciation of the letter D followed by a high front vowel (normally I, but also E when it falls in unaccented places). The letter T does the same thing (but goes to an English CH sound). We do this in English too, but unconsciously, when a Y sound follows a D: "Did you…" sounds "Dijoo..."

Other dialects like European and African Portugueses, as well as those of North(eastern) Brazil and Recife pronounce it without palatization (the name for that sound change).

It should but more likely in a sexual context.

Almost, because the final "m" is used there to nasalize the "a".

not exactly, listen to the slow version. It's pronounced as if it were gostão

More here:
http://en.wiktionary.org/wiki/Appendix:Portuguese_verbs