I believe that a makeup sealer is something you ought to look into. I would do a search in the makeup forum for makeup sealers or just sealers and see what info turns up, because I'm almost positive that I read that the sealers will help with the sweating issue.
If you have a checking account, you might be able to set up a paypal account. I don't know if that will work for ordering product online or not, but you oculd look into it. Another thing is a lot of companies have customer service phone numbers available on their site. You could call them to place the order and mail them a check or money order with the stipulation that they'll fill the order once payment is received. Or like Ali-kun suggested, other friends or relatives who would use their card on your order with you paying them back right then or finding what you want and having a local shop order it for you.
As far as brands, again, I'm not really the best person for makeup advice, but the two biggest brands I've heard of touted as very good are Ben Nye and Krolyean (sp?). I am positive that you'll find mention of both brands when you do the search for sealers
Hope that helps!