Can I take out life insurance on her to help pay for funeral and burial expenses?
Yes you may open up a life insurance policy on your mother.
You may buy the life insurance policy and be the payor of the policy while she is the owner of the life insurance. Just as if she bought the policy herself or she may sign for ownership while you pay.
However, if you are the person paying the premiums, you may want to be the owner and that way you can choose who is the beneficiary, to receive the death benefit upon your mother's passing.
Learn more about how to buy life insurance for your mother.