1997 Toyota Corolla Starter

Hello, today I tried starting the car in the mornin first time 1 click at a time and I got about 15 clicks before the car started then I turned the car off started again took anoher bunch of clicks 1 click at a time as I turn the key then I tried a 3rd time I got clicks then turned it off and you can here the engine still on but starting. Then I unpluged the battery cable for lil while and it happened again and I got it started with a loud noise for about 5-10 secs then the sound went away. I brang the car to a auto shop and they they got one click then it started which is funny nothin ever happens at the auto shop. So they replaced the starter and seems to be working fine. So far its working you think it was just the starter its the original starter and it has 118kmiles on it 11 yr old car. Do you think it was just the starter and I should be set? They checked the flywheel too and said its alright. What does the flywheel do? Ty