You have two choices - set up as a partnership or set up as a limited company.
I would recommend a limited company as there must be a fairly big risk of claims against the company for accidents and stuff like that. You will have adequate insurance, but just in case there is a problem, this limit on your liability would be valuable.
If you set up a partnership, the partners will be jointly and severally liable. So if someone wins a claim for €500k in damages, if her partner does not have the money, your wife would have to pay the full €500k.
It's probably an easier structure as well for clarifying who owns what percentage of the business.
I don't know, but I doubt if there is a requirement to register for VAT. Call the VAT office and they will tell you.
Brendan