If that insurance policy says 'up to' �20000 then it will almost certainly only cover the card it is associated with. Double check with that company though. (If he hadn't been paying the monthly payments it's probably invalid anyway)
I think the first step is to establish if there are any assets at all - contents of house, oddments in bank account, car, etc. If there are, the first claim on them is towards paying the funeral bill.
If there is anything left over then the unsecured creditors will get it - or more likely a small percentage each.
It might help to buy or get from the library a copy of the Which Guide to Wills and Probate (my rather old copy has sections on Scotland in it) or something similar.
If after reading through it you feel happy about DIY then go ahead. It's not difficult, but understandably some people feel that they have no time or cannot cope. Personally I found it kept my mind off other things and an interesting exercise, but everyone is different.
As to old debts, the law in England is that they cannot be pursued through the courts after 6 years from the last contact, request for payment, reminder, etc. Don't know if Scotland is the same. It may be worth doing a credit reference check on him to see if it turns anything up.
As to using a solicitor, it's up to you. It will cost you, with little chance of getting it back, and it's not legally necessary. But it could buy you peace of mind that no-one was going to come out of the woodwork and bite you.
The term in Scotland is Executor-dative, not Administrator, I've just read. It comes to the same thing though.