Great to hear you're planning to travel around Ireland. Ah, the midges. :) Yes, there are midges in Ireland indeed, but they tend to come out in swarms mostly during warm humid periods, especially after rain on a warm summer's day. I wouldn't say they are particularly bad, but I would advise you to use some of the readily available measures to prevent any biting, especially if you are sensitive to them.
Although there are some narrow roads indeed, generally speaking any area where there are sites that have space for motorhomes will have suitable roads. There are plenty of places throughout Ireland where it is possible to stop overnight with a motorhome, take a look at this link to an article on our website about Caravan and Camping
culture. There, you will find a link to Camping Ireland's web page, which has loads of information on sites available, and they also have a free app which you can download.
I would advise you to book at least the first and the last night, just to make sure you have a guaranteed spot to sleep after arriving and before travelling home again. It can be quite busy of course, so perhaps it's an idea to check a few nights in advance how busy it is in the area you want to go.
Wild camping is not uncommon around the country, just be aware that there may be by-laws prohibiting wild camping in certain areas or times of the year. Total Camping Ireland
has some more information you may find useful.
There are some threads that cover some similar topics with more information:
I'm sure our community members will have some more helpful suggestions too.
Good luck with planning!