It does look like a Spatiphyllum , common name Peace Lily. But it's not a Lily at all. It is an Aroid.
It actually looks quite good ! Definitely do not cut it flush with soil! It might kill it, at best it'll take ages to regrow.
Do not let it dry out, it likes to be moist and warm (above 70f , better 75-80f
).
Just cut the yellow and dry leaves close to the crown and give it a warm shower, leave it overnight in the shower stall after running hot water to steam it up: it loves high humidity and will perk up noticeably.
And do not separate it! It's fine as is. They really sulk after repot/messed up roots, it will look bad for 6 months..
Just give it some houseplant fertilizer once it warms up to 75f.. and water it sufficiently. So the leaves are turgid . Do not wait till they wilt. If it happens try to remember when you last watered, and next time water sooner ( water well to soak the root ball).