The yellow squishy cane is the oldest one ; they do die off naturally, and if grown in a dryer compost they just turn to something like straw . In the wetter compost they rot. No problem, just cut off at ground level, unless you are repotting, in which case cut through the rhizome to take the old cane away together with all its roots. You can be sure that the roots from that cane are dead too. I'm not sure which happens first, but whenever a growth is dead the roots are too - chicken and egg...
The leaf damage looks to be insect originated , but it is difficult to diagnose from a photo. Each brown spot is actually bacterial damage , the bacteria/spoilage organism entering the cells at the site of an insect puncture. Can't do anything about that once its done, except look out for critters - which can be microscopic !