Я очень интересуюсь русским языком or меня интересует русский язык - both are fine.

ведь:
1) as, because you know, eg. ведь он знаток — he is an expert, you know
2) but; why, eg. но ведь это всем известно — but everyone knows it
3) ведь это правда? — it's true, isn't it?,
ведь он пойдет? — he will go, won't he? - used for emphasis here

Выступать has several meanings, here are some of them that are mostly used:
1) project, protrude
2) go beyond borders
3) set out (military use). The 101st company set out first. - Первой выступила 101 рота.
4) speak publicly, make statements (Obama spoke to the Congress yesterday. - Вчера Обама выступил перед Конгрессом)
5) state one's view / position (Obama supported the middle class. - Обама выступил в защиту среднего класса.)
6) perform (in art and show business) , Sting is performing in London tonight - Сегодня Стинг выступает в Лондоне.

Оказаться
1) find oneself - I found myself in the hospital -Я оказался в больнице.
2) turn out, be found - He turned out to be very smart. - Оказалось, что он очень умный.
3) it appears (that), it turns out (that) - Вы, оказывается, всё знали — It turns out you knew everything.

тоже and также are very close in meaning. To use them properly one has to find them in some instances and compare (i think kp.ru will help), both of them are like 'also, too'...I think тоже is more closer to also and too, while также means more like 'equally, in the same way'. 

by the way, where in Russia have you studied ? your Russian is pretty good.