Read up on the Sex Matters website, and get clear on how your right to hold and express gender critical views is protected under the Equality Act 2010. I would read the Forstater judgment, but if you don't have time, I'm sure the Sex Matters website and other places will break it down.
And the Arts Council England case from the other day is a helpful example of a workplace situation that went awry too. The law is on your side.
You may well have to educate your managers/colleagues on the fact that gender critical views are protected under the Equality Act, and that while they may be concerned with offending trans people, they should also be concerned about offending gender critical people if anyone tries to tell you your questions are transphobic or bigoted.
Obviously if you do get any negative reactions, write everything down with dates, times, witnesses, etc in case you need it later.
On pronouns, I would just say "I'm not comfortable doing that", and leave it at that. I can't imagine they'll push it, but if they do, I would say "so, to confirm, are you saying I must disclose my gender identity to you?". Hopefully they'll back down at that point if they've had the inclusion training. Again if they are really clueless and continue to push it, ask them to clarify their request over email so you can consider it properly.