Do all Uk trains and train stations have baby changing facilities?

Most long distance trains and new trains have at least one toilet on board that doubles as a baby changing facility as do major stations. Of the stations and rail routes you mention Euston and Paddington definitely have baby changing facilities, so will the train from Chester to London.

Some of the trains from Paddington Slough (IC 125s) will have them too

I wouldn't go so far as to say "all" trains do - certainly some local trains won't, because they don't have toilets for anyone, but certainly the larger stations like Euston and, I think Chester, do, and so do Virgin Trains who you'll be travelling on between Chester and Euston. From the way you phrase the question, are you travelling on the Stena Adventurer, 8.20 a.m. sailing from Dublin Port? If you are, then the train from Holyhead to Chester is the Arriva Trains Wales service from Holyhead to Maesteg, and I honestly can't remember what the facilities are like (I was on it 2 weeks last Friday), but the class 175 is a nice train so I'd expect that it probably does have baby changing facilities. If you're doing that connection, I'd suggest you go straight from the ATW train to the Virgin train which will be waiting on platform 3 at Chester when you arrive, and grab a good seat if you haven't got a reservation, rather than go hunting for the station toilets (you'd have to go through the ticket barriers).

EDIT: Actually, there usually aren't more than a busload of foot-passengers on each ferry, so the trains aren't too badly packed leaving Holyhead (the one I was on got really full from Bangor onwards) - unfortunately most travellers seem to head for Ryanair these days, if they haven't got a car, so the ferries are more aimed at vehicular passengers which is why the ports at Dublin and Holyhead get really snarled up with traffic. At Dublin, Stena and I presume Irish Ferries, put their foot-passengers onto a bus which drives them onto the ship, and off again at Holyhead, to get to and from the passenger terminals. I prefer the Holyhead - Dun Laoghaire route because foot-passengers can just walk off a train, into the ferry terminal, and onto the ship at both ports, but unfortunately the HSS ferry only does one round trip a day now, rather than three as it did ten years ago.

Arriva Holyhead - Chester and Virgin Chester - Euston, WILL have baby changing facilities on them.

Train services on these routes are very modern.

I rarely use station toilets (a least 20p for pee is beyond the pale for me) but I can't remember being on a train in the last few years that didn't have a drop down changing board built into the toilet unit.

I don't know about the whole of the UK, Scotland, Wales, Northern Ireland & England,

But those you mention in England have,

Doubtful. Ask the rail company.