S197 5.0

I've got a 2012 s197 with the 5.0, recently have had a few issues.

Major thing, alternator went out. Stared whining for about 2 weeks before lighting up the dash "check charging system". Replaced that the same day and has been fine since though.

For a while now, it has had a bit of a weird idle, normal idle is 650, will spike to 800, drop to 400, and as of very late, will occasionally stall at idle. I dont notice this while driving, but it does seem a bit laggy at times. Im not sure if its the way I drive or what but it doesnt seem to get its full potential all the time. It does while im slowing down from driving drops about 100-200 rpm below normal idle before spiking up when I stop fully.

My research tells me TB dirty/damaged, spark plugs, vacuum leak, air filter. I did notice while changing the alternator out that the inside of the airbox was damaged, a piece about the size of a pencil fell out while I was taking the airbox off, I wasnt rough it wasnt from when I took it off. Im not sure if that's going to really cause this issue though.

I mainly want some 2nd opinions before I start buying stuff to replace, what are some easy tests I can do to see what may be the cause. I planned on getting a smoker as they are only $60 on Amazon for a cheap one, just have had to spend money on other areas and cant go blow it on a bunch of parts.

Local autozone has an airbox for $80, I planned to pick one up to outrule the airbox damage to start, then spark plugs and smoker, is at 112k so im sure plugs need to be done either way.