It's hardly 'luxury' toilets haha lots of new buildings have these types of facilities, and many current facilities can be modified (my university SU did just that, and they're hardly rolling in money).
Again with changing rooms, have more cubicles (that would be great, a lot of people don't want to see other people naked or be naked around them regardless of their gender).
Hospital wards I suppose are a little trickier, but again, there's very few reasons you'd actually be naked in front of other patients or need to see them naked, and you have privacy curtains. I imagine that most trans people would be as reluctant to bare-all to other patients you or I.
Once again, if someone is doing something inappropriate in these places, that is quite often a crime, regardless of their gender identity. If you noticed a woman creeping on you in a changing room, or being sexually suggestive in a hospital ward, you'd be within your rights to request that she be removed for indecency...regardless of whether or not she had a vagina.
Women's shelters you have 2 issues. 1 is that 'a man' is taking a space away from 'a woman', the second that a worker may be a man and trigger women.
The first thing I accept that I can't answer in a way that will be acceptable to you, because I view trans women as women.
The second, a person applying for a job has to go through an application process and an interview. They then will be accepted or rejected for that job, if they 'pass' so poorly that every person they help would know they were a man, then it's likely they would be found to be 'unsuitable' for that position. They would then have to prove that was because they were trans, which wouldn't even necessarily be the case.