He can use his NHS card here initially- it'll cover GP visits and I think medication too. But if it's an official move then depending on his income he could be eligible for a medical card. They are apparently bringing in a blanket allowance for all over-70s to have one but it isn't in yet.
The medical card would allow free GP visits and medication (excepting a dispensing fee per item of €1.50 IIRC), in addition to some other free health services in the community. If no medical card then you pay for any GP visits (in the region of €50-60) and for your medication up to a monthly maximum (?€120 or so)
Whether or not you have a medical card, everyone is entitled to free care in hospital- both inpatient and outpatient. There is a government levy on hospital stays of €75 per night but I think there's a cap on that so it doesn't end up ridiculously expensive. If you attend A&E with a medical card there is no fee however if you don't have one it's €100. I think this is waived if you have a letter from your GP. You can be referred to outpatient clinics and for any scans via the public system, which is free but can have horrendous waiting times.
If you want to go privately you can do this via your health insurance (rough guide could be €1000 per annum for insurance- just a guess, depends on age and medical history- you can get a quote on aviva.ie or similar to get an idea), or you can pay as you go from your own funds- this is reasonable if you want to get a scan quickly (€250 for an MRI with it being done within a week or so in a private hospital) or to see a consultant (€150ish for a visit), but if you need an operation then it becomes too expensive for most people unless they have insurance to cover it.
So in summary he should be fine- worth checking it out though- perhaps speaking to someone at the Social Welfare Office local to his wife-to-be.
Not sure about the property side of things- maybe someone else could advise?
Where is he moving to? Congrats to him and his future missus 