"I see that you are studying English." is correct. But "I see you are studying English" is quite common as well. "I see you studying English" Means that you are watching them study. XD

Continuous form (it's not a tense) is "[to be] + [verb]ing". "I see you studying English" is not continuous form. Aside from that, all your sentences are correct. Is there something else which confuses you?

I see that you are studying English!

It's a participle phrase. It's upper-level grammar.