The small cables are called patch cables.
You will typically plug the bass into the righthand socket and the pedal to the amp through the left hand socket.
You can (if you have the feature), use an effects loop. which is a cable look from amp to pedal(s) to amp, via two sockets, independent of the guitar being directly linked into the amps passive or active input.
You can get power supplies with a number of power jacks, yes, but a few pedals have different connectors. For example, a big muff pi, has a 3.5mm jack socket.
There is a typical order to pedals in the signal chain, but i am far to tired to get into that.