We are rushing to get a prototype out but now we're moving it to private for a few rounds of beta testing with real users. We've applied to some accelerator programs but I don't know if this is something acceptable to them over just going public on day 1.
Depends on the accelerator. I took part in an accelerator a few years back in which all the companies were still in ideation.
Do you know anything about what stage previous successful applicants were in? If not, maybe just reach out to the accelerator and ask what stage they typically work with.
It's good that helps you to validate the user needs; to meet their needs before building it...
No just improve