[cabletow]

Do some themes drain more battery power than others?

Do themes influence the ability of the phone to pick up and hold signals?

Logic tells me the answer to both these questions should be no but experience is playing havoc with my logic

[mgdotnet]

First question: yes - they could. Depending if there are animations/motion. If it is a large theme also with transitions that will play a role into it.

Second question: no - the theme changes the look for the device, doesn't change how the device reacts to connectivity to the network.