I see,我明白了,let's go to see a movie. 我们去看一部电影吧,如果强调持续一段时间观看用watch.
In general, we see a performance in public and watch a performance on TV. So for example:
- We're going to see a movie at the cinema tonight.
- We're going to watch a movie on TV tonight.
Let me see:让我想想,是idiom, 不可能 解释让我看看。Let me just see what the next song is?我来看看下一首歌是什么可以成立。
What did you write? is correct, when someone says What did you wrote? it shows that someone (speaker) is stupid. doubled negative in his thought.
I do love 我真的很爱... do 是加强你的情感“真的",不是助动词。