What does a notice of testamentary or administration means?

You do need to schedule a one or two hour meeting with a probate attorney to find out what to do. Any assets properly transferred to the Trust would pass as the Trust specifies; there should be a Trustee and alternative trustee named in the Trust. ?Insurance policies are paid out to the beneficiaries listed on the policy. The rest of his assets would pass as his Will states or as the state law on people without Wills states. The executor is the person named in the Will to carry out the provisions and the administrator is appointed by the Court to handle the Will. You can further read up on Wills and Trusts by looking at legal books by Nolo Press, etc. Testamentary means there was a Will.

The notices you asked about are probate notices. Probate is the court action for the transfer of property after a person dies. If you father's property was placed in a living trust, then a probate proceeding is unnecessary. With respect to an insurance policy, so long as there is a valid beneficiary designation then the beneficiary should be able to claim the insurance proceeds without a probate action or formal trust administration. You should consult a probate attorney about assistance with probate alternatives to get the insurance proceeds and any thing else that was in the trust.

A trust is designed to avoid probate. If Dad had no real property (real estate) why bother with a trust? In a small estate, assets can usually be collected with a small estate affidavit. No court is necessary. If the asset is a bank account, many big banks have their own form for small estates. Otherwise get one by googling or pay some lawyer $300 for the drafting.

Do you mean letters testamentary of letters of administration? If the policy is less than $5,000, then you probably don't need either, but merely an affidavit under section 13150 of the Probate Code.

I recommend shopping around. You may be able to find a local lawyer who would charge an amount that you feel is reasonable. It is hard for me to tell from your question what needs to be done regarding your father's estate. However, you should be able to get insurance policy forms directly from the insurance company.