Your old home in Dublin will require "landlord's / investment property insurance" once it is rented out (or other if it's unoccupied for a lengthy period)
You will need contents insurance for the house you rent in Longford if it's let unfurnished, otherwise no insurance as only the landlord has an insurable interest in the property and the contents (furniture, fixtures and fittings)
If you are doing a direct-labour self-build you will need some kind of "main contractor all risks" (wrong term but the closest I can get for employer's and public liability insurance on a construction site) for the new house in Longford and then regular re-build and contents insurance once you move in. If you have a main contractor over-seeing all the work you will need to check that his insurance is up to snuff, if you haven't done so already - ask to see the policy document, take a copy and ring and ask the insurer if it's current.
I'm not sure about the engagement ring.