TLDR Version: Although the graphic may suggest it, that's not what the TV Show host said, he indicated that the volcano is safely disposing of 'waste' power. (See video clip attached.)
If you listen to the Broadcast by the miniverse microverse1 residents, they explain that Rick provided the technology that provides electricity 'Powering our homes and businesses', 'while safely removing the dangerous waste power to a special disposal volcano.'
So, no -- Zeep isn't aware of the volcanic threat, as there isn't one described -- they thought they were sending 'waste' power to the Volcano, which Rick set up to be able to get rid of it for them.
That also answers your bonus question -- he didn't create a box to power Rick's battery because he thought the volcano was just disposing of their waste -- no need to use it since his 'new' tech didn't generate 'waste' energy.
Edit -- To address the expanded Bonus question: We don't know; possibly he will or did -- all we know is that power is being generated again. The simplest immediate resolution would be to return things to 'normal' by having people use their boxes again (which we see, along with a pissed-off Zeep, but that doesn't mean that's how things stay, given the time-compression they mention), but that doesn't mean he couldn't then profit by his experience and either
- Do exactly what you suggest and create two boxes (or just one and route some of it's power upstream to Rick -- think like a Pyramid scheme), risking facing what Rick eventually faced, when his new box develops far enough to build it's own miniverse, or
- Come up with a new way to generate power.
That said, the episode was showing scientists who didn't see the ethical ramifications of their actions, and how their creations mirrored them; Rick hasn't learned from the experience, so it's doubtful that Zeep has, either, except that he inhabits the first level of the smaller universes, and thus Rick can threaten him but he can't threaten Rick, possibly leading him to back down and just keep providing power indefinitely.
With luck, this could be explored in later episodes, much the way 'Ship in a Bottle' expanded upon 'Elementary, Dear Data' in the Star Trek universe; the show does do a lot of call-backs to previous episodes, so this has the possibility of being a plot-hook for a later episode.
Sadly, the video that was here (showing the transcribed segment, above) is now gone.
1 - Updated my terminology.. The first world was the Microverse. The NEXT one down the chain was the Miniverse.