ESA

Hello, ive had a letter from dwp, saying they need to look at my claim again, i think this is to do with the possible underpayments they have made over the years and has been in the news recently, i came off of SDA in 2014 and onto the ESA, im in support group, the letter has enclosed a form for me to fill in but its for the period from 2014 till now, i was however living on my own from 2014 till 2016, so about 18 months possibly they may owe me? but what i need to know is, do you know if i fill it in and i qualify for income related (on contributory at moment) will it trigger UC? also if i stay on contributory am i right in saying that this is NOT included in the UC payments? so contributory is not part of the UC? thankyou