Cherry tree in garden, compost or soil

hi, i am a complete novice when it comes to gardening however having recently bought a new build i am moving into this fascinating world

there is a cherry tree in the garden and i have been advised to remove it as it can get quite tall and the roots may go too near to the house or surrounding fencing and cause problems.

i have everything i need to remove it but it will leave a hole in the lawn turf, do i buy soil or compost and do you recommend any that are good?

the lawn turf is also a bit patchy in areas, i need to mow the lawn soon as its about the height of a can of pop now.  should i get some lawn seed to fill in these patchy areas?

do i need any specific soil for the lawn seed?

thankyou.