Petrol is about €1.85 at the moment depending on where you are I'm sure. Diesel is more expensive.
Primary school books are supposed to be free from next September I think. Lots of schools do a rental scheme. Secondary cost me about €750 last year (ipad and books) and €200 this year. Uniform (bog standard shirts and trousers, crested jumper and half zip pe top) was €150 ish.
GP care is free to a certain age but I don't know if it's up to 8 yet or not, it is free to 6. We were on a waiting list years ago for a paediatrician and having private health care didnt help. I've never really used mine for anything. There is some rule about health insurance coming from another country so I'd look into that specifically. You decide what level of cover you require so prices vary. There is private patient in a public hospital, semi private and private in private hospitals. If you are a private patient in a public hospital you still might not get a private room if there isn't one available. Private insurance is good for avoiding waiting lists for consultant appointments and scans and stuff like that. There is also the option of not having insurance and just paying private fees yourself if necessary.
I am with Tesco mobile and pay €15 a month for free calls and more data than I ever use. The €15 credit is there too so sometimes I knock another week out of it. My DM has a sim only plan which is all data all texts and all calls for €20ish.
Bank accounts. Permanent TSB have a cashback for every time you use your debit card thing up to €4 and the account is €5 a month or something like that. I pay around €5 a month for my AIB account.
Landline and broadband we're paying €55 for ours but includes a tv package. Lots of different deals out there including some incuding mobile phones and so on.
Bonkers.ie is a price comparison website for electricity, gas and phone lines. I had a poor experience with them lately though.
We have either an Aldi or a Lidl in most towns, plus a Supervalu - Irish chain which are mostly individually owned and can be hit and miss. In larger towns there will probably be a Dunnes Stores or both Aldi and Lidl. Tesco is only in big towns or cities. Marks and Spencer's only in cities except for a random branch in south Tipperary. I used to spend about €120 a week on food and cleaning and toiletries but I buy expensive food. It's about €150 now for 2 adults and a hungry teen. Aldi and SV own brand butter is €3.40 for a lb I think though possibly gone up to €3.60. A big head of broccoli is €1 in Aldi and €1.50 in Supervalu. Nine eco toilet rolls in Aldi is about €2.70 I think. 2kg of rooster potatoes about €2.50. At the top end of supermarket meat - 13.50 for the fancy aged Angus/Hereford fillet steak which I think is a 400g pack or two 7oz steaks. Small free range chicken about €5.50. 1 kg own brand sugar €1- 1.20. I buy a lot of gluten free stuff so I dont know how much a loaf of ordinary bread is. 6 organic apples are €3 in Lidl. 4 for 2.80 in Aldi , 4 for €3 in Supervalu but sometimes on 2 packs for €3 offer. Pack of 4 classic Magnums about €5.50, tub of haagen daz or similar 6.50 ish. You could sign up for online shopping and do a weekly shop and see for yourself.
It can be hard to get a GP or dentist as new patients but if your DHs childhood practices are still there it will be fine I'd say.
If you are below a certain income you can apply for free GP care and free prescriptions, or with higher income free GP. Prescriptions are capped for any household at €80 a month. Chronic illnesses or serious illnesses might qualify for free GP and free medication or other care. Things like physiotherapy or speech and language therapy have waiting lists so most people go privately. Health insurance might cover half the cost. I think most dental care is completely private but there is school dental care though appointments are years behind what they should be.