Alan welcome.
Quick answers
1 Yes you need to add paper, twigs, old leaves to balance the soggy green grass
2 All sounds good. Mow the large crowns of grass tight to the ground so mulches sit level over them.
3 Homeacres grass was like that 5 years ago, and constant mowing has resulted in what you see, with for example white clover that was not there at all. You could speed up that process by scattering lawn grass seed and a little compost in the hollows.
