Yes.
Women compete in a similar event called the Heptathlon that consists of 7 events.
First Day: 100 meter hurdles, high jump, shot put, 200 meter dash
Second Day: long jump, javelin throw, 800 meter run
Decathalon
yes
Mate selection is up to the female, and it is the females that compete for the males
They both do.
yes
Usually animals of the same species compete for mates { two males usually compete over one female.} Animals could compete over prey or vegetation too.
a decathalon in the Olympics
the males compete to fertilize
A decathalon
It happens. Particularly males fight and compete for breeding rights.
Yes they are allowed. However, not many participate.
Yes both males and females can compete in downhill skiing.