If you go back on the right after collecting the first charm, there's a bridge leading to stairs between the two hills. My apologies for the confusion; I suppose the bridge isn't eye catching enought and just seems like water or void.
Concerning the jump, you must collect 5 of them to unlock the temple, in which you can unlock the jump. I believe I could have made the progression a bit more clear and it could use some more indications.
Thanks for letting me know about the issues, it's always great to get some feedback !