Hi Chris,
Thanks for your post and welcome back to your PPL training!
I am a professional pilot (and aircraft owner). I have just a simple SEP, fixed gear, fixed prop. It gives me a lot of pleasure but financially it makes no sense at all!
Your aspirations are clearly at a higher level and I am sure you will enjoy owning and operating a Cirrus or Malibu. The costs will be high but you will have a very capable aircraft which will be fully capable of your 'mission', including flying across to France.
Now to try and answer your specific questions:
1/ Sorry, no idea. I live in France and my private flying is in the south of the UK.
2/ I would hope that a modern school would include GPS training but you will have to do some research to find the right location with the right fleet and equipment to meet your needs.
3/ I wouldn't say it's a pipe dream but it will be expensive!
4/ Bit of guesswork here but:
Hourly operating cost £300
Hangarage: £2500 p.a.
Maintenance: £5000 p.a.
Fuel: included in the hourly cost.
Insurance: £3000 p.a.
Fees: included in the hourly cost
So, total cost for 150 hours per year = £55,500 £370 per hour.
As I say, a bit of an educated guess on my part, based on 'scaling up' my costs.
It might be worth visiting likely airfields and chatting to the guys in the tower or clubhouse. They can put you in touch with owners of similar aircraft. There may be relevant adverts on the notice board as well.
As others have said, I wouldn't worry too much about the aircraft used for training. Get your PPL on a clapped out old spam can and then buy your Dream Machine, employ an experienced mentor-pilot and fly with them for 6 months.
Good luck and let us know how you get on!