either I'm blind or it's NOWHERE to be found unless you join a multiplayer server with that car. That would also make offline practice impossible, is it supposed to be like that? Where can I see penalties outside of the game?

I dont undestand what your asking.

Weight penalties and air restrictions are only in the RB4(actually doesn't have any), FXO and XRT. When online you press F11 to see what the restrictions there are for that car.

There are no restrictions for hot lapping, just racing online and it's only temporary as well.

I think thats right.

You can see them using the network debug function, if you join any host at all.

How to do this :

1) Press SHIFT+F8 to turn on network debug
2) Join any host or start your own host

You will then see these messages :

Handicaps :
XRT : mass 20 kg / tres 0%
FXO : mass 70 kg / tres 3%
XRR : mass 30 kg / tres 0%
FZR : mass 80 kg / tres 0%

Imho it would be better if the penalties would be shown in LFS World for example.

Maybe a tab in the Racers & Hosts online window could be good place for them.