How long does it take for a player to receive a report notification from Riot?

Depends, I've usually gotten a response within 12 hours. Remember that if you are e-mailing on the NA server that they are probably open 9-5 Monday-Friday. Just to give you an idea.

it ranges on when the problem is handled. It can range from a day to 30 seconds.

There is alot of background inner works. but its essentially first come first server kinda rules.