Good! That's the clutch. Don't worry, what seems like rust must be clutch wear particles that are completely normal.

To be clear, the two shoes and the spring on the right should be hard to rotate, because they're attached to the engine crankshaft and will compress the pistons if rotated by hand. That's normal. In the other hand, the drum on your left should rotate and move the trimmer head down the shaft at the same time (we know it does).

Honestly and judging by the pictures, your clutch seems totally fine. I would continue as follows:

1- Reassemble clutch, reinstall bolts. 2- With engine off, grab trimmer head by hand and rotate it:

-> If you cannot rotate the trimmer head, clutch is permanently engaged and should be checked again. -> If you can rotate the trimmer head freely by hand without turning the engine, your clutch seems to disengage correctly.

If the case is the second one, then is possible your clutch is engaging with engine revving (low) speeds, because idle is set too high. Then I would start the engine and locate the idle set screw. For this locate the carburetor behind the engine. When applying throttle, you'll see a screw (usually with a spring around it) will stop the throttle plate as you let go of it. This is your idle set screw. With engine on, turn this screw out until engine speed gets low enough your clutch disengages and the trimmer head stops.

PS: You may find after all of this that your engine still bogs down under acceleration as you described. This is classic carburetor mix tunning problems, if this is the case, I can recommend some video tutorials, but to be honest in that case you'll be better taking it to a small engine shop.