Can you transfer characters from gta 5 on the ps4 to another ps4 account

I'm afraid this is not possible, no. Your progress is irrevocably locked to the specific gamertag you made that progress on, and can not be transferred to another gamertag, like you would be able to with just transfering to another console.

Quoting from Rockstar Support:

"When transferring from PlayStation3 to PlayStation4, you must use the same PSN ID. A new PSN ID on PlayStation4 cannot be transferred to from a different PSN ID on PlayStation3 since your characters progress is tied to the PSN account."

Yes you can actually, you need to transfer your character to Xbox, then from the Xbox you transfer back to your new ps4 account

Yes you can just call rockstar support and tell thim you want to switch a character to the other profile and they will take care of it