As Firoball suggested it is a nice way to implement the gravity change as a double jump.

There is one big decision that we have to make (as soon as possible):

1) The game focuses on puzzle oriented gameplay.
2) The game is primary a jump'n'run (maybe with adventure elements) with puzzles.

If we went for 1), in my opinion we should follow the concept of brother-sister and their special and different (!) abilities.
"There she needs to kill herself in order to follow her brother" haha that is a bit extreme? That is somehow too sad I think, not a bad idea though.
I think that the robot is not the best choice for the main character, I fear then it would be hard to create an (emotional) connection to the real player. Limiting the gravity ability to special spots (metal/ magnetic/ ...) may reduce the possibilites and the fun in using this feature.
We could implement nice puzzles and riddles with two characters, but it could be that this concept turns out to be kind of slow.

2) If we chose the second variation the game could become fast and thrilling with the alternative period of time where the player gets haunted (have a look at my 3rd last post including this one). The calm age could be filled with puzzles and the like. There should be some friendly NPCs or imagine the player could control several instances of himself for a short time to solve riddles!
I took the time and created a new prototype of 2), watch it here:

New Video

The gravity change ability is limited to standing on the ground and the time travel part is realized by portals.

Furthermore we could take into consideration to invent (!) new creatures that don't look like human beings/ animals - without question the drawings above are nice!
For example the well known chinese dragon as a source of inspiration:



What do you guys think, 1) or 2) ?
I would prefer 2) (not just because it was my idea but I would prefer that type of gameplay, especially when you consider long-term fun and motivation).