Balance transfer is only to transfer from one credit card to another credit card. For eg., if you are paying 12.99 APR on Bank of America cr card, you can balance transfer the balance on the card ( $10,000) and avoid incurring interest by balance transferring to 0 APR cards like chase slate, chase freedom, Amex blue card, capital one platinum to name a few. Chase slate provide 0 APR and $0 balance transfer fee, while chase freedom and Amex blue provides $200 or $300 (I don't exactly remember) fir first $500 you spend. And capital one is only for about 9 months 0 APR and then after high interest rate.

Yes, most of the companies ask you either you want them to pay your cr company or they will ask if you want them to write you the check and you will pay. But I am almost certain that you will have to tell them account number of high APR card to verify that you are not lying. They are not writing you check like that ;). And I don't think they will write you the check of entire cr card amount. For eg., $10000 out of $10000.

 Hope this helps.