Are rear derailleur universal?

[PiKe]

I inherited a bike which was a bit beat up and unloved.

The rear derailleur high low limit screw has been physically bent and it was a swine to get out, I only have one screw now which means the chain can fall off the smallest cog, are these screws universal or failing that, can the derailleur be replaced with any other, or is the teeth spacing/count specific?

 

[PiKe]

The brand is just "Power" and there isn't a derailleur bracket, it seems to be part of the frame.

I can't see a third adjustment screw either.

Don't really want to spend a lot on it as it's pretty rusty but still.rides ok.

 

[PiKe]

Wow that is vintage! 6 speed?
it looks like the hangar is integral to the derailleur, and bolted to the frame.

I'm not really sure to be honest - all I can suggest is to point you here: https://forum.cyclinguk.org/viewforum.php?f=5&sid=79e737099427d5530b202b2c5b53a6cc

I'd ask there, helpful crowd and some of them have encyclopedic knowledge of this kind of thing. It might be you can just source a new screw if the threads aren't damaged.

Thanks.