The three of you explain to the solicitor what you want to do.
1. Transfer house into your name.
2. You are paying your siblings cash
3. You will be taking out a mortgage to cover the portion of the purchase that you do not have the funds to cover, and home improvements.
The solicitor will advise you all on how to proceed with the title change and the house sale (transfer) to you. The costs involved, who pays the costs, the estate, you or the three of you equally. If the money you are using to pay your siblings is coming from your parents estate, the solicitor can arrange for them to be paid directly form the estate.
They will also advise on revenue tax requirements if you exceed the €325K life time allowance.
What you are proposing is something solicitors dealing with probate come across all the time so it should be straightforward. You will need a solicitor to do the title transfer.