Most iPhone screen repairs can be completed within 30-60 minutes, depending on the repair shop and the availability of parts.
Immediately turn it off and avoid charging it. Bring the phone to a repair technician as soon as possible for water damage assessment and possible repairs.
It depends on the cost of the repair versus the value of the device. If the repair costs are reasonable and the phone still meets your needs, repairing an old iPhone could be a good choice.