Hi Ray!
I think I can answer your questions pretty simply here. :)
1) As presented above, the insurer may pay the insured up to $9500 still. Bear in mind that the intent of insurance is to bring you back to the place you were before the loss occurred. It is not intended to bring you a profit but simply replace what was lost. They are not obligated to pay the full $9500 if you don't end up spending the full $19K on repairs, but would typically pay you at least the $7500 remaining of the Actual Cash Value settlement.
2) You can spend whatever amount you want to do the repairs, but the insurance company will pay no more than the total of the loss $19,000 minus your deductible of $1,000. So, total, they could pay out up to $18,000. Theoretically if so far the plumbing and water mitigation total $6000 then you would have $12,000 left that would be covered by the insurance payment to do your repairs. You can spend over that $12,000 if necessary, but they typically would only pay up to that total of $18,000 I mentioned as the deductible will always be applied.
2b) If you have what is called "Guaranteed Replacement Cost" then they would pay whatever it cost for the total of repairs minus your deductible. Not many insurers like to do Guaranteed Replacement Cost so it may be unlikely that you have that type of policy, but it is a valid question for your agent/the claims department.
3)Again, theoretically, they will be making another payment to you of $7500, regardless of receipts. If you spend under the $16,000 they pay under the Actual Cash Value payment (i.e. no depreciation reimbursed) then you get to keep the remainder... so say you end up being able to get everything done for $14,000, then you get to keep the remaining $2,000 which is not technically a profit, just that you were able to do the repairs in a more cost-effective way than the standard market price. That stated, yes, you are correct, in order to recoup the full $2,000 of depreciation, your total receipts would need to equal at least $19,000. That stated, if you submit receipts of $18,000 you should still be able to recoup $1000 of the depreciation... meaning it's not all or nothing in terms of recovering that portion...
Hopefully the above makes sense. If it made it more murky, perhaps someone can explain it in a different way...ha.
All the best in your claims process!