Hello, I'll do my best to answer your questions although do bear in mind the NHS is a huge and diverse organisation and what may be true from my experience/in trusts I have worked for may be totally different in other places!
In general I would say you are well qualified and if you have your PRINCE certification and a good general background and experience in PM work you shouldn't need to go in at Assistant level, although what an 'assistant' is varies from place to place, sometimes on a large and complex programme an assistant might have the responsibilites (and pay etc) of someone titled
'senior project manager' elsewhere - so I'd go off the actual JD/advert and grade to guide you as to suitable jobs rather than the job title per se. That being said a lot of roles are advertised internally so if you find you are struggling to get a foot in the door (and can afford to), taking a slightly more junior role with the aim of quickly progressing can be quite a good idea. NHS experience is very much valued in general.
I would say, the NHS in general and PM work specifically does support a good work life balance and is satisfying. Of course the work can be intense, pressurised and frustrating in a typical public sector way (trying to achieve a lot with very little money/resources, constant drives for 'efficiency', shifting sands of political priorities and headache inducing bureaucracy and slow pace of change being typical complaints), and some people do work very hard and long hours, there's a general expectation that you will muck in in a crisis and be able to occasionally flex your working hours to get the job done, plus of course as anywhere you get the odd nutter manager or power tripping supervisor who refuses to adapt to modern working practices but in general I would say that most people work reasonable hours and have the flexibility they need to look after their families. Annual leave, sick pay, maternity pay and pension are excellent, things like paid carers leave and flexitime vary trust by trust but usually are at least as good as in the private sector, and flexible working, part-time working etc are fairly well supported and becoming increasingly the norm.
Home working is an interesting one, until Covid hit I'd say the NHS (and I'm talking in general here, cf my point above re the diversity, I'm sure there were trusts that have always been hot on this) was behind the curve for how well home working was supported - couple of factors, hospital trusts in particular still had a general expectation that everything and everyone happens on-site at the hospital and the idea of a dispersed workforce was quite alien to them, plus the NHS chronically underinvests (or worse, mis-invests) its IT budget and so the technology to support remote working was patchy. E.g. only a few years ago one trust I knew still had 90% of its workforce using ancient desktop PCs and landline phones, very few laptops/mobiles were available, and their remote log in software was 10 years old and buggy as hell. Even if your manager was relaxed about home working it was a real battle to be able to actually do any work at home so it was very much an ad hoc thing for most people and it was a vicious circle in that you struggled to be productive at home, so you were expected not to do it too often, so there was little incentive to improve etc. Pleased to say though that Covid has done us a favour here and really kicked everyone into gear to sort out the situation, and now every NHS non clinical/office worker I know is fully home based for at least the next 6 months and planning to continue substantial home working for the foreseeable future. Don't get me wrong, there are still lots of issues and some managers that really don't like it and are itching to get their teams back into the office but I think you stand a much much better chance of getting 3 days a week home working agreed now than before Covid where you quite possibly might have been looked at like you'd grown an extra head for requesting such a thing 
Travel is another very much trust by trust/role by role thing, NHS England and other national roles do generally have a travel expectation built in (in normal times anyway) because of the nature of the work and the teams being spread across the country. Some CCGs and CSUs now also work in a similar way with regional hubs and expectations of regional travel. Most hospital trusts however usually have 1-3 sites all within a fairly close radius of one another, and you won't normally be expected to do more than go up the road to the other site (usually no overnight stays unless it's something like the cornish trust which covers an enormous geographic area) so again if this is important to you you'll need to get a feel for the requirements of the specific job.
Good luck!