[kaisen]

It appears to be exactly where it's supposed to be. No timing issue. If it had slipped 3 links, it likely would not run.

If I had to guess, your issue is valve adjustment. Most Corollas of that vintage (guessing 1998-2002 there) had fixed (non-adjustable, non-hydraulic) bucket shims. They were set perfectly at the factory. Over time, with heat cycle, wear, and abuse, the clearances can be too tight or too loose.

Too tight and the valves won't seat completely, causing poor idle at best or melted/burnt valves at worst. I've rebuilt or replaced several of these motors for that exact reason. You might be "catching" the symptoms before real damage is done. It's common in all Toyotas that use this family of motors (but Toyota is perfect, right?)

Too loose and they rattle with the slack. Probably not "hurting" much in the short term, but causing some accelerated wear and inefficiency.

If you check them all with a feeler, you'll find that you have some that are tight, loose, and in-spec. Measure how far out of spec they are an order the correct spec from your Toyota dealer (although they are usually cheaper at your Chevy dealer, as it's the exact same motor as the Chevy Prism).

Sound about right?

It also looks like you have lots of sludge/heat/bad oil.....