Why won't my washer machine motor, gearbox, or inside basket free spin
It is normal for resistance to be felt when attempting to rotate the motor driveline attached to the gearbox. Gearboxes have a fair bit of friction and are attached to a rather heavy tub. This machine is equipped with a tub brake that is supposed to engage during the spin cycle if the lid is lifted. The spinning stopping fairly quickly is normal. Continuing to spin indicates the brake has malfunctioned. I'm not sure if you are referring to the wash or spin cycle though. If it was wash cycle, it does sound odd, but I doubt the coupler would be at risk.

When off, the inner tub should be difficult to turn, but it should turn, you are turning the entire drivetrain and motor rotor. It cannot be deduced that there is a problem with the motor or gearbox with the information given, but I think failure of either is unlikely. I'm actually not hearing anything indicating anything is seriously wrong at all.

Since you asked, a new gearbox mail ordered in the US has a list price around $200 plus shipping. I would expect a rebuilt one to be 2/3 to 3/4 of that. Replacement is disassembly of the whole tub/agitator assembly, a fair bit of work.

Interestingly, another person is having difficulty with his Kenmore machine not spinning. It's well known that Kenmore appliances are rebadged name brand appliances. The parts diagrams of his and your machine look remarkably similar, if not identical. Probably an unrelated problem though, it's just curious.