does the rebate get credited back into my visa account
No
will they send me a cheque (check), made payable in USD?.
This second option wouldn't be much use to me, due to me not having a USD bank account or a US address
You've answered that one!
I was wondering if the store managers are open to negotiation for giving a cash discount rather than the mail in rebate
Probably not - mail-in rebates usually come from the manufacturer, not the retailer.
Sorry...