Learn Russian: Богатый турист покупает сувенир.

In Russian, adjectives must match the gender of the noun they describe. Because турист is a masculine noun, богатый takes the standard masculine singular adjective ending -ый.

Does покупает mean "buys" or "is buying"?

It can mean both! Russian doesn't have a separate "is doing" (continuous) tense in the present. Depending on the context, покупает translates to either "buys" or "is buying".

Сувенир is the object being bought. Why didn't its ending change?

You are right that direct objects take the accusative case, which often changes a word's ending. However, for masculine nouns that represent non-living things (inanimate objects), like сувенир, the accusative form is exactly the same as the basic dictionary form.

Since турист and сувенир look like English words, can I just pronounce them the English way?

They are borrowed words with the same meanings, but you still need to use Russian sounds! For example, турист has a rolled "r" and an "ee" sound for the и. Also, pay attention to the stress: in сувенир, the emphasis falls on the very last syllable, unlike in English.