For the console, 6v is the highest voltage that's advised by Davis. Any higher will shorten the circuitry life. A little extra will probably take quite a while to cause damage. But I know that a 7.5v DC adapter that was rather stupidly substituted for the official Davis adapter by a particular reseller caused damage in a relatively short time.
ISS I've not seen any official Davis recommendations for, but I'm guessing not to exceed 5v. (But 5v adapters are two a penny these days, so that shouldn't be much hardship. That said, IIRC you do need one with the right-angle plug to connect easily into the SIM board.)
Battery powering via the DC jack input is a bit more tricky. I think I'd be wary of using say 2 x 18650 or LiPo cells in series, but say 4 x D cells might well be OK. I'm not sure whether it's feasible to inject say 3.7v from a single 18650 via the DC jack - there may be a voltage regulator that's expecting 5v as a minimum, but I don't know fir sure.