Can I use my PS3 remote control on my PS4

No, you can not because they are for different consoles.

Sadly the PS3 Media Remote will not work with the PS4.

The PS4 Media Remote, while being "official" and endorsed by Sony, is a very poor substitute for the PS3 version. It does not allow for volume punch-through for an amp, contrary to what the manual says. It could not switch inputs on my SONY amp, which is mind boggling.

Avoid the PS4 Media Remote. You're better off using the included controller.

No, a PS3 bluetooth remote will not work on the PS4.

However, in October 2015, a PS4 remote was produced and the functionality is similar to the PS3 remote.

You can find them on Amazon or a number of other shops that carry Sony products.

Yes, download ps4 remote play to your tablet or computer, sync your ps3 controller, and go to your settings on your ps4 to enable remote play and sync your tablet to your ps4 to start using your ps4 with a ps3 controller. It doesn't work with vista, xp, or others, it uses mac or windows 7-8.