Peridot assumed since Steven is a Rose Quartz he'd be able to repair the Galaxy Warp. I don't think Stevens healing is specific to Gems I'd assume it's able to repair Gems and some Gemtech/Entities which follow the same principles of a Gem.
The Warp Pads pre-date modern Gem Technology, before Gem Tech and their advancements in Powering Tech. It's highly likely that the Warp Pads are powered by a Gem Based Power-Source as these seem to be fairly popular at this time of Gem History, therefore Stevens Healing Powers if they were active might of done something to atleast temporarily jump start a warp pad even for a short period of time maybe a couple of seconds if that...
I think the Geode is a power core for the warp pads. Pearl says that the storm inside the Geode can vaporise them and she's also talked about how dangerous it is in warp space, plus there's a storm going on. Also we've only ever seen the Geode when the warp pads have been a factor in the episodes. We first see it in House Guest, when we learn about the warp whistle, and we see it again in Warp Tour so perhaps the crewniverse are trying to show a connection between the two of them.
I mean it's only appeared when the warp pads have been a main focus in the episode, not just being used to transport the gems to the places they need to go. In the two times we have seen it we learnt something new about the warp pads and the warp pads were a driving part of the episode.