Yes, the on the wheel the caliper is defiantly stuck or pad is broken,when placing your hand on the rim its like putting your hand in a hot frying pan.
Get it up in the air, supported by jackstands.
Remove the caliper and try to compress it. It should be relatively easy. If it's not, while compressing crack the brake line or the bleeder loose at the caliper(sometimes the
line is the better choice as bleeders can be rusty and break easily). If it goes in, the brake line is collapsed. If not, either the piston is seized OR the slides are giving you trouble, clean then make sure they are lubed.
When it's up in the air(steering wheel free, unlocked), grab the tire at 9 and 3 and shake gently, there should be no play. If so, then physically look at the inner and outer tie rods, and check the LCAB's to see if they are soft. The E36 racks tend to take a shit IIRC on the right side, the rack inside gets loose and moves, it happened on my M3. Then the 'rebuilt' rack I got had the same issue when I installed it.
Next, grab the wheel at 12 and 6, and shake it. If there is play, check the ball joints in the LCA's. And a less likely problem would be the strut mounts.
If you see nothing but there is still play, as mentioned above it could very well be the wheel bearing.
It wouldn't hurt to re-balance the wheels also, just incase.
After any front end work down, have it aligned. Make sure they do the rear also as the E36 has toe-adjusters on the rear trailing arms.
And the engine noise, can't do it by video.