Can someone in US pay dollars directly into my Nigeria bank account using PayPal?
So long as you open a PayPal account and link it to your bank account there should not be a problem. Be aware that money arriving in your PayPal account will remain there until you choose to transfer it to your bank account. Also be aware that such transfers attract a fee from PayPal. This being the case you really ought to charge Jeremy a couple of hundred dollars more if he wishes to use PayPal rather than Western union!