Whether the machine or stand is level doesn’t matter. As long as you’re just using the level to compare the different components. Still really tough to tell with a bubble level. I have a digital level I picked up from Amazon which works really well:
https://smile.amazon.com/dp/B0148M7P4O/ref=cm_sw_em_r_mt_dp_ZAV81BWQEQGX9MNBPYKD?_encoding=UTF8&psc=1
Much easier to read the exact difference.
It’s nearly impossible to insert the bit wrong. It’s not like a drill chuck that you can get it off centered when it’s wide open. But when you do that you know immediately. You’d definitely notice the vibrations. It could be badly machined, but it still wouldn’t cause the issues you’re having since it’s spinning - the angle would be changing as its spun around.
It’s hard to tell from pictures but it does look like you’re not perpendicular. Spin the bit as you look to check.
If you don’t have play in the bracket then just loosen the mounting screws (assuming that you’ve checked that the x-axis is parallel to the spoil board (search for tramming if you don’t know how) If it isn’t/you haven’t then do that first), square it up and re-tighten slowly and in a couple steps each from just tight to fully tight. You can probably use the side of the module to check instead of the bit.
For play in brackets check this thread:
-S