My experience with all EU providers so far is yes, you do have to prepay, I think Hetzner for exemple was 20 euros when I signed up years ago?
Most likely they are unwilling to let customers pay later without any guarantee that they're good faith and solvent. Maybe it is a cultural thing? It's only my personal opinion but it never struck me as unreasonable.
Nope, not common, except for prepaid mobile plans which are kinda ubiquitous.
I have never had to prepay anything for Hetzner, not 20y ago for servers and not for the last 5-7 years for Cloud VPS. Maybe for recent-ish signups?
Some hosters support prepaying (for example INWX where I have my domains) but I am reasonably sure you could also do other forms of payment