Low Idle Issue

#1
2008 Toyota Corolla S, auto trans, about 80k miles

Noticed my idle would be a little low while riding a week or so ago, give a slight shudder/vibration. Well this morning I changed the oil and cleaned the battery terminals, and now it idles even more rough. Only idling at about 600 Rpm or less and vibrates a lot more, even will almost die at some points. Any quick checks I can do to maybe narrow down the cause or anyone with similar experiences.

Never changed spark plugs or adjusted valves to this point, issue just started about a week ago and suddenly got worse after an oil change.
 
#2
And of course now that I've let it sit for an hour it's not as bad as it was. But it is still a little rough, not quite smooth or as high as it used to me, just a subtle vibration.
 
#3
Also side note, found a clamp lose on the air intake on the engine, tightened it up before parking it when it was running like crap, but again after sitting for an hour, back to the less terrible idle
 
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