You may check with other roofer or handyman, estimate a price to fix the corner shingle. I guess it wouldn't be complex and expensive.
Regarding changing the gutters, the market price of installing 125 - 200 feet of new gutters is approximately $1050-$2400 based on different materials, minus depreciation, keep $1500-2000 is fair to me but not $7000.
When you negotiate with that contractor, ask a deadline at the same time and tell him you have to hire somebody else to fix if he couldn't make before the deadline, then you won't return the rest of money.