Should I keep my Android tablets' power off or leave them on standby mode?
Turning the tablet off at night will most likely extend its life, but this defeats the purpose of having a tablet, since a key feature of the tablet is instant power-on from standby.

Generally, there are two things that drain the battery of any device: the display (when it's turned on), and any wireless communications (3G, WiFi, etc).  If you really want to conserve power at night time, turn off the tablet's WiFi and 3G (airplane mode).

The power draw of the CPU and RAM is negligible compared to the power consumption of the display and wireless comms.  And it's normal to feel a little heat near the CPU, the wireless antenna, and the battery when charging.

I wouldn't worry about battery life, in terms of charge-discharge cycles, unless you plan on keeping your tablet for 20 years. The same goes for the MTBF of the physical components.

The flash memory will not go bad if the tablet is left on. In fact, the tablet probably reads and writes to flash more when booting up than when it's idle.

Generally, I would suggest enjoying the tablet the way it's meant to be used!  If it breaks because of normal use, then it wasn't worth having anyway!