Actually I only see one piece of romex in the panel. The white cable coming in the top with the bare ground.
It is a sub panel and that explains the separate neutral and ground bars.
The neutral looks like it is being fed with the two larger white wires landing on the right
The two pole breaker may well have the same size wire just different insulation types. Look carefully and you will see that the smaller dia cable is spliced to a thicker cable. Looks to me like TW insulation as opposed to THHN. Not a big deal to me. Just means the panel was replaced at some point and the wires were too short.
The National Electrical Code does not disallow splices and or wirenut’s in a panel. The biggest question I would have is why the two wires on each of the main lugs? That is odd. As far as I know The NEC has never allowed conductors smaller than #1 to be paralleled. The other odd thing is the color combinations, black/red, black/red.
My guess is that is either a parallel feed or there is a large load being taped off of the main lugs. Regardless, what you have there is a code violation.
I would be very leery of adding an AC condenser load to this panel.
Not sure what you mean regarding the bushings. The NEC does not require them in this application. Any "clamps" would be ouside of the panel and not visable.
Looks to me like the wire in the main lugs is #10 wire with old cloth insulation. #10 is currently good for 30amps.