"It is a long time since he didn't study English" is a very awkward
sentence. It almost feels like "since" is being used like "because"
here. "It seemed like it had been a long time since I missed my cat so
much." I.e., "it seemed long because one was missing someone". "since
he didn't study English", with the negative is difficult. Its
ambiguous. For instance, maybe it took him a long time to graduate
because he didn't study English? Or maybe He has been studying English
for a very long time, and it's been a long time since the time when he
didn't study English. Or maybe, you could be trying to say "It has been
a long time since he stopped studying English."
"It's two months
since you didn't come to see me" also isn't a great sentence. "It has
been two months since you stopped coming to see me." Or "It has been
two months since you last came to see me." Or "It took two months
because you never came to see me and help me shorten the time."
Anyway,
all your other sentences seem good and I'm sorry I didn't read the
grammatical notes more carefully. Actually it seems like this
discussion might be quite helpful to Chinese English learners.
Also, you should check out tatoeba.org where you can register and translate sentences into Chinese or look up usage for English words.