Yes it is perfectly fine in my opinion to apply for full time if want part time, I would never have found a job if had only applied for positions advertised as part time.

I have never negotiated as such, as I always went into interview them knowing that I wanted part-time. Then in the interview I stated what I wanted in terms of days hours (and travel) and do their offer was made on a full understanding. The last role they wanted 5 days, I said ideally 3 but would do 4, they wouldn't take 3 agreed on 4 they offered 5 short days instead of 4 but I didn't want that.

I suppose I have never thought of it as a negotiation more I state what I will do and then if it works for them they accept it. 'Negotiation' of part time I see as more of a thing if in a role and want to cut down hours or coming back from maternity leave. When you are in a role is easy to negotiate because you know the job and what can be done in the part time hours you want and they know your skills so are in a strong negotiating position. When are not with that employer you have very little to negotiate with which is why I see it more as you state your position and they either work with that or not. My experience has been many companies are flexible with hours, e.g. start and finish times but far less so with wanting three days a week for example. I have not got to interview for many contracts because I don't want full-time, but often if their mindset is five days a week you can't shift it.

Do you know someone in your industry can ask? I was a bit clueless in mine at first, but now have helped a couple of people get part time in roles similar to mine, just by being able to explain what approaches to part time work.

I have read people say don't specify until offer many times but I think it probably can be industry/role dependent, certainly my area - declare (rather than negotiate) at interview or earlier works best.