Yes, the missing shingles are a problem; they will allow leaks in the next rain.
My roof had considerable damage from the wind today too. I think one bundle of shingles will repair it and than's far less than my $500 deductible with Farm Bureau.
The average life of the new fiberglass shingles is 12 to 20 years. I know, they have a 20 year LIMITED warranty (notice one word is larger than warranty). Roofing companies can show you at least 15 things you didn't do according to the instructions, thus voiding the warranty.
In your case I would recommend removing the old shingles and replacing them with new ones. Take several detailed pictures of the roof and see your agent (check your deductible first) and you may even want to get an estimate of the cost first. Your agent knows several roofing companies that work well with him and will be glad to tell you their names.