Also, how do I time those exercises that need timing?

For planks and things like that, I generally take my watch off and put it on the floor where I can see it.

Timing to music also works, if you've got a song which you know is roughly the right length (or where you know that up to the first chorus is x amount of time, etc.), and can sometimes be more motivating than staring grimly at your watch *g*.

I know they don't have any in the women's.

*glares at them*

and discovered a resistance band in a drawer when looking for a place to store the mat.

Yay, resistance band! That gives you many fun options for things to do at home.