Yes. You don't have to physically touch it to own it. There is a concept of "clearing", once the money clears it's yours. The dispute is if it's enough to avoid clearing payments, or if you should avoid taking any orders altogether.
> It would be the equivalent of delegating that responsibility to a non-jew. I don't know how would that be ruled, but I remember reading that it's allowed to let non-jew servants perform tasks on the sabbath, though I have no idea if it's accepted by the Hasidics.
The rule there is not in dispute, Hasidics are the same as any other observant Jews.
The rule is you can not pay a non-Jews to work specifically on Sabbath. However you can pay him to work, and let him decide when to do it, as long as you give enough time to complete the work not on the Sabbath, if he decides to work on the Sabbath that's none of your concern, he's not Jewish as is not required to keep the Sabbath. You can also pay by the week and then the payment is not for the Sabbath.
Incidentally a slave (even a non-Jewish slave) is not allowed to work for you on Sabbath, also animals are not allowed to work for you. Computers however are not alive - automatic processes are unquestionably permitted. AI (if it's possible, which I don't think it is) will be very interesting.