Welcome to my forum. Glad you are enjoying looking around it.
First the VAT. You do not get a refund on anything you "consume" such as B&B, hotels, food, car rentals. Gifts you purchase and export back to your home country (outside the EU) are eligible for the VAT refund.
Most B&Bs will take your credit card details to make a reservation but prefer to be paid in cash upon departure. Those that do accept credit cards for payment often tack on an extra percentage (2 -3 %) when using a cc to pay for the room.
Assuming you are in the US or Canada, using Pay Pal means a foreign exchange. I'm not sure of their rules on that so you will have to go to their website to find out.
Some people use vouchers that they pay for in advance but I'm not an advocate of them. It greatly reduces your B&B choices to those that accept them, the B&B only gets a percentage not the full amount and travel agents take a cut.
When I'm in Ireland I usually just get cash from an ATM and pay that way.
It is just not feasable for many smaller B&B owners in Ireland to take credit cards.
There is a minimum 3% charge on all transactions they accept (which they seldom pass to the paying guest). There are also other fee's involved in the membership of the scheme, the rental of the equipment, the phone calls made to the premium rate modem which transfers and aproves the transaction. US cards are not Chip and Pin so the old fasioned process has to be carried out and may take up to 10 days before the transaction is completed (possibly for inexplicable reasons declined?). You will find that larger B&B's and Guesthouses (B&B with more than 5 letting rooms) that accept cards are at the higher end of the price scale, partly because they do take CC payments. I did work it out a few years ago for a friend considering the option and the cost of running a card payment facility could have been equivelent to paying the wage of their breakfast waitress (12 hours per week)
As Michele has said it is as easy to just pay cash on departure. If booking through a web site then payment by card would be accepted or some like Go Ireland then a small deposit is taken.
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Two rules for Ireland, Take your time & bring a sense of humour