- If this medicine will get rid of my headache, I'll take it right now.
- If this medicine gets rid of my headache, I'll take it right now.
- If he will see me at the station tomorrow, I'm doomed.
- If he sees me at the station tomorrow, I'm doomed.
I think that these questions are really about idiom. That is, they’re not really about the very general rules that govern the English language, but about the way that native speakers would express these particular thoughts or understand these particular expressions. I’m afraid, though, that I may be the only native speaker for whom I’m speaking. Perhaps that will be for others to judge.
SENTENCES 1 AND 2
If you scrutinize the first two sentences through the lens of grammar, you wonder whether the speaker plans to take medicine only after it has got rid of his headache. That excessively cautious approach to medicine seems stronger in #2, because “gets” is present-tense and “I’ll take it” is future-tense. But if I heard someone say #2 I would defend the tenses to mean that if this is the sort of medicine that typically cures headaches, then I will take it. I think that both sentences are pretty unremarkable in normal colloquial speech, but one of them might possibly get a laugh in some very nerdy circles. And in edited writing perhaps #1 is better than #2, with the still better arrangement “I’ll take this medicine right now if it will cure my headache.”
SENTENCES 3 AND 4
As to the next pair, #4 seems more idiomatic to me than #3. I cannot defend it, but that’s how it seems to me.
I think that in general, I would say “If he sees me” before any consequence that relates to the time after he sees me. If he sees me, I will tell him that I got lost. If he sees me, then I will run. In these sentences, what happens in the “then” part happens after he sees me; so “sees” is in the present.
On the other hand, I would say “If he will see me” before any consequence that relates to the time before he sees me. If he will see me on Friday then there’s really no need for me to visit him before then.
This seems to associate the earlier event with the present tense in each case, and the later event with the future tense.
So in the sample sentences, “being doomed” seems to be a later development. The same would be true of approximately synonymous results. If he sees me, “then I’m sunk,” or “then I’m finished,” or “then it’s all over.” All of these state the consequence in the present tense grammatically, but what is more to the point, they would all put "sees" in the present tense.