My lender told me how much insurance to buy. Is that enough?
It is enough for them. A lender requires cover protecting its loan and has no interest in your liability limit, your belongings or where you would live during a rebuild. Meeting the requirement is the start of the conversation rather than the whole of it.
It comes out of escrow. Can I still change it?
Yes, at any time. You choose the insurer, not the lender, and escrow simply pays whoever holds the policy. Because the bill is invisible, these policies go unreviewed for years, which is the main reason to look at it deliberately.
What should I check first as a new owner?
The liability limit, whether contents are replacement cost, and the loss of use figure. None of those were the lender’s concern and all of them are yours. They are also inexpensive to improve on a modest house.