Part of the problem with living trusts is that unless they are properly funded, they are just pieces of paper until funded. I trust there was also a Will. If there was a regular Will in addition to the Trust it may say who gets what. If there was a simple pour-over Will, that essentially puts everything that the deceased owned not in the Trust into the trust and thus funds it, and the trust beneficiaries inherit the whole thing.
The named executor has no legal duty to serve if he does not want to. If neither he nor other family members for whom he feels a duty or responsibility are beneficiaries, or he is on the outs with the beneficiaries, he can turn down the "honor" and refuse to serve. The court would appoint another person.
If he starts to serve and is appointed, he ought to hire counsel, whose fee should be paid out of the assets of the estate and can advise him on the process and handle matters. This is particularly important in multi-state situations. In California the probate fees are set by law.
The first question to consider is where the deceased lived. If he was a Californian, a California probate is called for, so hire a California probate lawyer. If there is real property in Indiana, then ancillary probate also could be needed in Indiana. If it is just stock and accounts, that is handled from California.