How would I go about making sure that there is no legal problem when I have to stop the service (for whatever reason) and drop my paying customers? Is a simple sentence in a Terms of Service page enough and does it depend on my country of residence (I'm from Germany)?
I was thinking about only offering monthly subscriptions, so that nobody would have to pay too far in advance in case I have to quit the business. Is that a good idea?
Setting up a help page pointing to similar services would be nice. Example https://www.mapzen.com/blog/migration/ And with GDPR in mind a way to export data. Also privacy related make clear who now controls the existing data (you personally is fine, deleting all is fine, some users worry it gets sold).
If you registered a company (UG, GmbH) then for tax purposes you might need to proper shutdown the company. There's processes and form for that and you might need to submit annual accounts for several years even if both income and expenses are zero. With German UG you're still personal liable should any customer demand money, let's say they sue for damaged and however unjustified you then have legal costs more than the company has on their bank account. GmbH costs 25000 Euro to setup so I assume with bootstrapping you don't go that route.
When we were still bootstrapped companies flat out asked us how long we existed (e.g. 3 months) and what guarantee there is we still exist in 6 months. It's a stigma but people have been burned with startups in the past.