First, welcome to the ACA Forums! Next, a warning that bicycle touring really gets into your blood and could become an obsession.
To answer to most of your questions is it varies. Are you going to do paved touring only? More "mountain biking" on mainly gravel or dirt paths (this is also called bike packing)? Do you have health issues that might require you to get an electric assist bike or a recumbent trike in the not too distant future? Whatever you decide, I strongly recommend you start by buying a used decent bike to ensure you 1) like bike touring (people tend to love it or hate it); 2) don't waste a lot of money on depreciation if you only keep for one summer; 3) decide a different style bike is what you want; etc. You can get a good used touring bike for around $1500 that could easily be the last bike you will need if it is the right one for you. NOTE: Do not try to rig a road club/racing bike to tour if it does not already come with built-in rack mounts as the frame is either too short (heels hit the packs) and/or not stiff enough.
Accommodations in Europe (and to a lesser extent in North America) range from "stealth" camping (hiding in woods), to campgrounds, to indoor accommodations. Indoor accommodations range from albergue/l'auberge/ hostel (dormitory style) to pension/gite/chambres (typically a private room which may or may not be in a person's home) to hotels/motels to resorts. Note that in campgrounds, you may be charged for each item, i.e. a tent site, a fee per person, the shower, electric, laundry, etc. but they are typically a little cheaper overall than a North American commercial campground.
The best way to find an informal group in advance it to ask around. For instance, you can post a "companions wanted" ad (free) in ACA's Classified section here on the forums and you can write in and have one included in the monthly magazine (don't know if it is free) but you most likely have to be a member of ACA to get in the magazine. Other websites also have a "companions wanted" section such as BikeForums.net; CrazyGuyonaBike.com; various Facebook sites, etc. Don't forget to see if the various European bike websites like Cyclists Touring Club in Britain have a companions wanted section. Usually, a group of 2-4 is a good start.
You don't say how long you want to ride in Europe for, i.e. 1 week, 1 month, the summer, etc. One option to possibly consider that could give you flexibility is to ride the Camino de Santiago in Spain. While 95% of the people walk it, I rode it this summer. There are towns about every 3-6 miles which typically have a Auberge and a restaurant/bar (tavern or pub). Something 200k people do a section of the Camino per year and there was never a day I didn't see a dozen other cyclists so you could ride with others as much or as little as you want and not worry about not meeting someone else the next day.
Spain is a scenic country, relatively cheap, drivers are very courteous, and the towns along the Camino are used to bikers and hikers. It would take about 2-3 weeks to ride it the main Camino from St. Jean Pied de Port (in France near the border with Spain) to Santiago though there is probably a dozen Caminos to choose from. After you do that (recommend mid-May to early June or after mid-September departure due to summer temps in Spain), you would have your "touring legs" under you and could venture out on your own.
Touring in Europe is easier overall than in North America if you want plenty of services as it is much more densely populated than North America. I speak only limited Spanish but can get by in Europe with the help of Google's Translate app; a godsend for this Okie who can barely speak proper English. Honestly, if you know how to do the minor repair on your bike (flats; adjust derailleur & brakes; clean/oil the chain; etc.) you can do Europe (or North America) on your own. Europe has numerous trails, paths, and routes to enjoy. Check out the EuroVelo routes for easy planning.
Finally, you might try posting something on the International ACA Forum but it is very little used. You would have much better luck with international touring info over on the BikeForums site as it is more international that the ACA website. This site primarily address ACA's vast route network and touring in North America.
Again, welcome, and Tailwinds, John