I've not seen infection where an arm has been severed (eyes are the most common problems) but watch for a swelling at the damage site. Tetracycline is available for fish without a prescription but determining dosage and successfully getting an octopus to ingest it is a lot of experimentation and second guessing.
There are no known, externally obvious features to declare an octopus as female.
Here is a link with pictures to help determine if an octopus is a male. Try to observe the third arm on the right (ie clockwise as you orient your eye with the octos). If the animal is a sexually mature male, you should be able to notice that he keeps this arm curled most of the time. The tip of this arm (hectocotylus) is also suckerless and modified to be somewhat funnel shaped (
ligula not often easy to detect). Additionally, there will be a channel that runs down the length of this arm that is sometimes detectable.