This is my opinion which isn't shared by everyone but I let the chain tell me when it has to be replaced. The big hint is how far from TDC the crank sprocket is when the cam sprocket is at TDC. More than 4* off at the crank means it's time for a new chain. The other hint is chain guide wear. Unfortunately much of the front of the engine has to come off to replace the chain guides. If the engine had regular oil changes with good quality oil I'd be surprised if the chain needs attention. This 606 with 277K miles has but 1* of chain stretch - E300D timing chain stretch

603 oil leaks - check the front crank seal, vacuum pump main gasket and vacuum pump brass cover fitment, belt tensioner arm attachment to the engine front cover, cylinder head near the #1 exhaust runner, IP where it meets the block, rear main seal, turbo oil supply and drain. This isn't common but my belt tensioner damper gave up and spilled fluid on the front of the engine.

Speaking of belt tensioner, that's something to keep an eye on in a 603. Release belt tension and check that the tensioner arm doesn't click as it pivots and doesn't wobble. Check that the tensioner pulley spins smoothly and quietly and doesn't wobble. I'd put my money on keeping the tensioner in good order before messing with the chain.

ACC fan control is independent of vacuum. The fan is positioned vertically and the armature(?) shifts as the bearings wear so the brushes don't make good contact. And the brushes simply wear over time. Sometimes the fan will get squeaky, sometimes it'll come on at high speed but not at low speed, sometimes it'll take an upwards kick under the passenger side dash to get the fan started. You need new brushes and/or bearings or just replace the motor. It's not difficult to move the blower cage from the old motor to a replacement motor, or you can buy a motor with cage attached.

Yes, ACC vacuum leaks can cause transmission shifting problems. Find the line from the engine vacuum pump to the cabin. It goes through a yellow (or green?) check valve ahead of the brake booster. Cap the line and see if shifting improves.

Sixto
87 300D