As mentioned in comments, more context is needed. However, I can't envision a scenario in which sentence 2 would be good.
You are talking about two events, studying English and seeing your teacher, and you are trying to relate them in time and characterize them. Each is a separate event, so to some extent, the tenses used can be different and specific to the event, it is not a case of parallel construction. However, you're relating the two things in a single sentence, so there is some influence due to the context; they are not completely independent.
"Had <verb>" means it happened in the past but not anymore. The only reason to use "had" rather than simply past tense ("I studied English", "I saw my teacher"), is if that status is important. In your example, it might be true that you also haven't seen your teacher again since then, but that isn't really the point of the sentence. If it is additional information you're trying to convey, it would be better to be more explicit:
I had studied English after seeing my English teacher, who I haven't seen since, by the way.
Your history of visitation with your teacher is an unrelated subject, so if it is important to include it in the same sentence, it needs to be more of a stand-alone thought that you connect. My reading of your original sentence is that this visitation history is unnecessary to your point; the only relevance of seeing your teacher is that it happened before you studied English.
If your visitation history is relevant, using "had" there doesn't adequately convey that because there's no obvious connection, so it interferes in the sense that it makes the reader stop and wonder why "had" is there; is there some additional meaning that they're missing. It becomes a stumbling block because it seems out of place.
Sentence 1 is on the right track, but awkward. I'm not sure whether it actually breaks any grammar rules, but "I had studied" and "since I saw" don't seem to go together. Even if it is technically correct (and I'm not sure whether it is), it is an unnecessary complexity of tenses that doesn't sound right to the ear of a native speaker. The natural way to express that would be either
I studied English since I saw my English teacher.
I had studied English since seeing my English teacher.
Both versions are still slightly awkward and could be polished to sound a little more natural, but they are grammatically correct and make clear that "studied" was in the past and happened after seeing your teacher. The second version makes it explicit that you didn't study English again after some point in time, which may or may not be important.
Note that you could also substitute "seeing" for "I saw" in the first example. Repeating "I" is part of what makes the sentence awkward.
Note that "since" has several meanings. It can mean "because" or "more recently than". Another variation would be to substitute "after" for "since". "After" could also imply "because", as well as simply indicating chronology. The chronological meaning of both have a subtle difference. "After" means that it followed in time. "Since" means "more recently than". It's a slight difference in perspective.