Good morning and welcome
You will find as many opinions as there are members on those questions but as someone who spends over half the year most years in Europe I can tell you how we survive:
1.
Solar panel fixed on the roof - removes the need for hook-up. We have an 80 amp panel and just the one leisure
battery and it meets our needs - but others will recommend a couple of both (or more!).
2. We call in at (cheap) campsites when we fancy a lingering shower - although for a small fee I can tell you where you can get good free showers in France (on the other hand, see my final comment!) or when we want to do the laundry. Then we use hook-up.
3. We don't have a genny - having camped in remote quiet spots and had a van+genny turn up next to me it is one of those rare times that I briefly want the return of capital punishment for idiots! - but this is an aspect of your request that will probably lead to war among the various pro and anti factions.
4. Internet - there are various wi-fi hotspots (especially the car parks of MacDonalds) and libraries have internet (often free).
5. Gas - DON'T take Calor because it cannot be found in Europe and you will just be carrying around a hunk of useless metal. Again, there will be lots of conflicting advice about which cylinders/regulators to get - so take your choice. CampingGaz is almost universal across Western Europe but very very expensive. If you are going to do this a lot then I recommend an LPG system (such as Gaslow, which we have, or Alugas). LPG is widespread across all of Europe but ironically most difficult to find in the most visited country - Spain. But even in Spain it is not a problem if you plan ahead. LPG systems are expensive initially (ours cost £400 to supply and fit) but rapidly pay for themselves in cheaper gas (ours paid for itself inside 18 months).
Finally - don't forget that most of Europe actually welcomes motorhomes (unlike this miserable country!) and if you look up the website
CAMPINGCAR-INFOS you will find free or cheap aires not only in France (some with showers!) but Spain, Portugal and the rest of Europe too. There are other websites - look at the country forums on this website.
Happy travels
John