I attach my probes with hot glue. Apply hot glue to the cord and not the probe itself. You can do the same with tape. Do not use aluminum (foil) tape as it will mess with the thermostats readings.
Your snakes will be able to breathe, the tubs aren't air tight.
Holes in the tub are used to adjust the humidity in the tub.
More holes = less humidity
Less holes = more humidity