Open source? not sure there are some good with everything you mentioned but if you just want a noncustodial option, there's Coinbase commerce. Have you looked into it? You can accept USDT, and I believe they have an API as well, if you want to automatize some things.
Yeah I do.
But Coingates fees are the highest.
And also have country restrictions.
I'd like to offer my services worldwide.
I'm talking about Coinbase Commerce, and not Coingate. I'm guessing you're referring to this list? https://coingate.com/supported-countries
I don't think Coinbase has such limitations. As for the fees, it's a flat 1%. You can read more about it here: https://help.coinbase.com/en/commerce/getting-started/fees
I have 2 challenges with Coinbase:
1) they still do not offer USDT (including many blockchains)
2) Its US company where I need to fulfil additional requirements. Cannot do it atm.
In the case of private gateways, do I only always have access to my wallet or is the seed in the hands of the company?