1)You can lodge the cheque without any commitment. It is an initial payment and is not in full and final settlement. So if you lodge the cheque and later decide you want more, then you can apply for more. But you keep the €10,111.
2) You were on a fixed rate from 2007 to 2012 and should have gone on to a tracker at ECB +1.15%. Being overcharged by €9,200 seems small.
3) I expect that not only have you received this cheque, but your mortgage balance has been reduced as well.
4) What lender are you with? My guess is that it was AIB or EBS.
5) How much was your original mortgage?
6) Were you in arrears at all and if so, by how much?
Brendan