Overmind states that it gains a power counter for each unused MU. Does this take into account MU that can only be used for a limited number of programs (i.e. Djinn's 3 extra MU)? Yes, Overmind gains power counters from any unused MU (from such sources as Deep Red). Djinn does not work, however, because it does not provide extra memory.
A Runner has Deep Red and 3 icebreakers installed, none of which are Caïssa programs. Additionally, no other programs are installed and there are no other MU bonuses (i.e., Dyson Mem Chips, isn't Chaos Theory, etc.). The Corporation uses 1x Bad Times. What happens? The Runner can choose to lose the MU from Deep Red.