Hi! I’ll try and answer your questions.
A. Talonflame’s Weaknesses
As you mentioned, Rock Slide is very bad for talonflame. Fake Out is also bad because it removes gale wings and takes away a turn of setup. Another weakness of talonflame is its relatively low base attack, but this can be overcome. A quick glance at Pikalytics (A website for Pokémon usage stats, it’s vey helpful) tells me that the common Pokémon that can exploit talonflame’s weaknesses are Tyranitar, Rillaboom and Incineroar.
Of course, Talonflame is very weak to stealth rock, but nobody uses them in VGC anyway.
B. Good Teammates for Talonflame
Looking at talonflame’s threats, Rillaboom, as you mentioned, is checked by talonflame anyway, so You need a way to deal with tyranitar and incineroar. A very niche pick would be Hitmontop. It offers fake out to help setup, wide guard to stop rock slide, and close combat to hit both incineroar and Tyranitar hard, not to mention intimidate. However, Dynamaxing Tyranitar will destroy both fake out and wide guard, so you might be better off with redirection, but keep in mind that rock slide will beat ridirection.
If you’re using an offensive Talonflame, a defiant Pokémon is probably good to scare off incineroar, because talonflame already has low attack. I’d pick Passimian over bisharp or braviary because braviary plus talonflame equals very bad rock slides, and bisharp is weak to incineroar anyway. Passimian, however, counters both incineroar and Tyranitar.
If you’re using a support talonflame, I think that Water Urshifu would be fantastic because priority tailwind means it can outspeed cinderace, and adamant expert belt is a OHKO even when Dynamaxed (no bulk). It also counters Tyranitar.
C. What Talonflame set is commonly used
This question is easy, Pikalytics says that Talonflame’s most common move is tailwind, with taunt being up there as well. Dual wing beat is also used to OHKO whimsicott through sash with priority. This shows that it’s usually support, but it has some offensive usage.
Hope I helped!