1) The insurance company will probably want to make out the check to her individually. you can still deposit the check into the estate account either way. It is a good idea to set up an estate account.
2) The executor / personal representative for the estate can sign over the car to a beneficiary. There are some forms from DMV that are helpful. The title should not have to be titled in the name of the estate first. Remember to contact her car insurance company asap.
3) Yes, your mother's expenditures that are on behalf of the estate can be reimbursed (therefore not part of her inheritance). Save the receipts until the estate is closed.
4) The probate rules allow a reasonable fee. She does need to receive her appointment authority from the court. She should ask for non-intervetion powers.
I'm very sorry about your sister's death. It sounds like it was very traumatic.
You have a practical problem here. If I understand correctly, your sister's estate is worth approximately $8,000. It could cost almost $700 just to initiate a probate proceeding ($350 court filing fees plus the cost of filing the "Notice of Petition to Probate Estate" in a "newspaper of general circulation" in the county where your sister lived - the newspaper filing fees vary depending on which newspaper you use).
By law in California the lawyer's fees for assisting in a probate are set by statute. In this case the lawyer would be entitled to 4% of the value of the probate estate - which would be approximately $320. I don't think you're likely to find a lawyer who's willing to take the case for that (and legally, the lawyer cannot ask you to pay more without violating of the State Bar's rules on legal fees for probate cases). If your mother were the executor, she would be entitled to exactly the same fee.
So you definitely need to find a way around having the health insurance check made out to your sister's estate.
I strongly suggest you try submitting a "Small Estates Affidavit" to them (Cal. Probate Code section 13100). The requirements for the affidavit are set out in Probate Code section 13101.
If they balk at transferring the payment to your mother using the affidavit, I suggest referring them to Probate Code section 13105, which states that if they "unreasonably refuse" to turn over the funds, they are required to pay all of your court costs and all of the legal fees you incurred in obtaining the court order requiring them to do so. That usually does the trick. In fact, I usually quote that code section in bold in my cover letter.
As for the DMV, it has its own "small estates affidavit" form. You can use the same format for the health insurance rebate. I suggest having the signature on the health form notarized, though.
The California probate code also sets out the "priorities" for payment if there are insufficient assets in an estate to pay all of the creditors. See Probate Code section 11420. Taxes must be paid first. Then come "expenses of administration" - which would include the clean-up costs, etc. Then come funeral expenses. And so on.
So your mother would have the right to recoup the expenses she paid unless payments owed to a "higher priority" creditor exhaust the estate (much like a bankruptcy situation).
This information is not intended to substitute for professional legal advice and does not create an attorney-client relationship. You should accept legal advice only from a licensed legal professional with whom you have an attorney-client relationship.