If we travel the 3rd week in May on the Wesr, south and East. Do we need to have reservations
That's heading into peak tourist season, so you might want to at least book your first night somewhere. You shouldn't have trouble finding places, but if you want a good choice, booking ahead would be good. On one of my trips, in April, we had some reservations, but twice we booked via phone in the morning for that evening.
Not critical. You can arrive in town early afternoon in most places, go to the local TI, and ask them to help you find accommodations. You'll be sure to find something that time of year, and this approach will allow maximum flexibility in your travel plans (a good thing when touring Ireland).
On the other hand, if you are picky about where you stay, you might not be able to find the most desirable (to you) place with this approach. Also, arriving at a town without knowing where you will be staying requires you to spend the first couple hours of your visit getting oriented and making those arrangements.
I've done it both ways, and will continue to do it both ways.
We traveled last August and had no difficulty finding great b and b's to stay in. When we arrived at one that didn't have availability, they recommended another. The trip worked out great.