I know several websites you can check out but I am not sure if they meet all your requested requirements or if they support all countries.
Fees are different and I didn't compare them in details so you need to make your ownresearch.

- Coinpayments is based in Estonia (I think) and they exist from 2013, accepting Bitcoin and many other coins; other websites are using them for years;
- Coingate is based in Lithuania and it was created in 2014, accepting Bitcoin and over 50 other coins;
- Coinbase Commerce needs no introduction but I think they don't have custodial wallet like you want.