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According to my runs and to this version of the holy texts fan community-sourced spreadsheet guide:

- Inviting Sayra: Idk if throwing a refused invitation does anything with anyone else than Jasper, but it's definitely not an absolute necessity to get Sayra's friendship (and you don't necessarily need to invite her to any event at all if you play other cards right.)

- Sayra's secret: She approaches you late in Week 6, a little before the ball (guide says morning of Fire day), and tells you her secret if you're close enough to her and have figured out the existence of the rebels faction from the secrets chain (from exploring the castle in previous weeks).  So first you figure out the Rebels secret, and on Clarmont's route you get the talk, with zero mention of Sayra until W6.

When you say "I still couldn't choose the "participate in rebellion"", what's your exact issue? Do you not get the option at all, or does it show up but Clarmont refuses?

-You get the dialogue option about how you can't know his problems if he doesn't tell you (and he breaks up with you immediately):

You failed to get the entire Rebels secrets chain.

(OR maybe you didn't get enough Rebels approval? I don't think so, I'm not certain but I believe my horrible horrible widow who managed to promise to support him didn't have Rebels approval and got Clarmont and Sayra rivalry.) (And then betrayed the rebels and her beloved to Gisette.)

-You tell him that you know exactly what his problems are and get a long talk, but the option to say "I understand" or "I refuse" to break up doesn't show up:

You picked too many wrong answers in the previous dialogue.

-You can say you refuse to break up, but he breaks up with you anyway and you don't get the options to offer to help him:

You don't have enough Persuasion (guide says 400 needed). Even if you picked all the right choices and know everything you need to know, you still also need 400 Persuasion.

(Usually you'll need to have gathered a lot of Manipulation and Insight at the very start of the game to achieve this.)

-When you refuse to break up, the options to help him do show up, but if you pick either option, Clarmont refuses and your narration when you go to sleep references "your break-up":

You didn't pick enough right answers in the previous dialogue. 

(There are scene-ending answers, wrong answers, neutral answers, and right answers. You can manage to get far into the talk with a few wrong answers, or with just neutral answers, and then suddenly get shut down at the end because you didn't make enough actually good points.)

-The option to help him shows up, but if you pick it, Clarmont says he'll need to think about it, and when you go to sleep afterwards you get a line about how "things are still so unsettled" with him:

You have succeeded! He'll come back to talk about it some more in the next week, and you will get a scene with Sayra a few days after that. You're clear to go!

-When you pick the first option, you get the "break-up" narration line, but when you pick the second option (to support him without getting involved in the rebellion), you get the "things are still so unsettled" line:

This option has lower requirements than the option to help him. This means that the reason you can't make the first option work is that you are not ethical and/or you have not picked a few but not enough right answers.

You have succeeded at this option, though! You can keep going down this route and get a good ending anyway.

Good luck!! You can do it! And it's totally worth it, bringing peace to Revaire is SO satisfying :)