If you have no preferred pronouns, just say (none) or something
This will help make people feel more comfortable in this comm and has a side effect of showing you support trans people when making comments in other communities. It will also make reactionaries seethe and make it easier for mods to purge them, and make trans people feel safer all over the fediverse.
No, they don't. I personally know a cis person who has their pronouns on hexbear set as they/them or comrade/them. Those aren't the pronouns they use in real life.
If someone assumes you're trans simply because your pronouns are set to something other than she/her or he/him, that's kind of on them. People are allowed to lie on the internet. Choose any pronouns you like, it doesn't matter.
I personally assume absolutely nothing about the cisness or transness of someone with "any" or "none/use name" as their pronouns of choice.