Yes usually, the home insurer has the 'interest noted' on your policy of the lender, you can change that.
The life insurance may be assigned and you can get the assignment released, usually you need the permission of the lender you are leaving to remove the assignment but not in all cases, things seem to have changed in some places. I was able to cancel assigned policies recently without anything from lender needed, life company said it had changed that requirement!
Equally the new lender may not be assigning policies either, you may just have to give them proof that you have one, best to check with all the parties involved what their actual procedures are.