If I understood the sequence of events correctly, your letter should look roughly like this:
I'm writing to report that I've already sorted out the problem. Thank you for the suggested solution. I had tried this solution before receiving your letter though.
Using the Past Perfect is okay here: you're mentioning an event in the past: trying out the solution, and then a subsequent event: receiving their letter.
You may use did try to put more stress on the fact that you tried this solution:
I'm writing to report that I've already sorted out the problem. Thank you for the suggested solution. I did try this solution before receiving your letter though.
But did try would look better in a letter telling that you still haven't sorted out the problem, as a way to reassure them that you've indeed tried it.
If you use "I have tried that" it will look ambiguous: the construction will leave them guessing when exactly did you try the solution: before you received their letter with the suggestion or after.
It's not surprising these confuse you. There are actually three different idioms involved in your list, expressed in different combinations.
GET to VERB means, as you say, "HAVE the opportunity to VERB".
PRESENT: I get to go. = I have the opportunity to go.
PAST: I got to go. = I had the opportunity to go.
Pr/Past PERFECT: I have/had gotten to go. = I have/had the opportunity to go.
('gotten' is US; in BrE this would be 'got')
HAVE to VERB means "must" (used nowadays only in the present tense) or "BE obliged to VERB".
PRESENT: I have to go. = I must go.
PAST: I had to go. = I was obliged to go.
Pr/Past PERFECT: I have/had had to go = I have/had been obliged to go.
HAVE got is a replacement for "HAVE" in two uses: 1) the "possess" sense and 2) the "BE obliged" sense. It is used only in the present tense.
1) "Possess": I've got an old car. = I have an old car.
2) "Be obliged": I've got to get a new car. = I must get a new car.
It's even possible to combine the HAVE got2 idiom with the GET to idiom.
I have simply got to get to go to Disneyland! = I simply must have the opportunity
to go to Disneyland!
There are lots more idioms using these two verbs, but it would take me all night to go through them, and it would probably confuse you even more.
Best Answer
"Will I have to...?" asks if it will be required in the future at some point - not if you are expected to do it right now.
"Do I have to...?" is more flexible, it asks if it is required now - but can also be used of known requirements to do something in the future.
If unsure, prefer "do I have to".
Separately, "come there" can seem a little awkward. The rules of when it's better to use "come" or "go" are somewhat tricky. Any of "come along" (if you're both going to the meeting in the same direction) "come to you", "come to the meeting", or just "attend" might be better.
Also consider "Would you like me to..." or simply "Should I...?", as "have to" gives a faint impression you'd rather not be at the meeting unless absolutely necessary, whereas you may prefer to convey a willingness to come.
As you put it later "Am I required to be there?" is perfectly fine.