Мне - Indirect object.
Меня - Direct object.
This use of достаточно, as well as of many other similar adverbs, results in the noun taking the genitive form, which, in some contexts, is considered partitive. With the affirmative есть, such a change does not occur.
Yes; a preposition is required for that purpose.
You will often read or hear that there is no English equivalent. To get a feel for the pronunciation, your best bet would be to visit Forvo and listen carefully to words ending in ы.