אני חושב שהשחקנית הזאת משחקת היטב
Yep, please report.
What does היטב mean, how is that formed? Is it a process you can apply to other adjectives as well?
It's היטב heitev. It means "well", and no, it can't be applied to other words.
If טוב applies to the (female) word משחקת, why is it not טובה?
Because it's used as an adverb here, I guess. Adverbs usually don't change for gender or number, as far as I know. Can a native speaker confirm with more examples?
I am not a native Hebrew speaker, but I can confirm what you said. It is an adverb here, and therefore it doesn't change.
Shouldn't it be באופן טוב ?
can הזו and הזות be used interchangeably. Do they mean the same thing except that one is more formal or less "street".
This is a poor translation. A person 'plays' a game of football but an actress 'performs' well in a play.
I was wondering about that as well, but I have heard Israelis use לשחק with reference to an actor performing.