basket, accidentally deleted my post while editing, on mobile then press wrong
you can do remote play under 2 conditions
1. both your vita and ps4 are using the same psn account
2. your ps4 is on standby mode
i tried remote play while i was outside before using vita -> tethered wifi (my phone) -> ps4. played both driveclub (on disc) and warframe (f2p shooter).
apart from eating quite an amount of data and some occasional input lag, everything else works just fine. if you are on a proper wifi connection with a good speed (e.g friend's house), you should be able to play the games without any problem.
of course, do note that both the image and audio are compressed while playing through remote play. so for example if you are playing driveclub on your vita, the graphics definitely won't look as good compared to playing it on the ps4.
during your first time setting up, you will need both the vita and ps4 to be on the same network in order to pair the consoles together. below is the link to the guide
Using remote play via the Internet | PlayStation®Vita User's Guide