yes yes and yes include pirated games (so called fake pkg or fpkg in short)
you can jailbreak ps4 (any model) as long as they currently have 4.55 firmware or below.
Jailbreaking PS4 is fairly easy at the moment, there are various ways to jailbreak it but the fastest way is to update your Ps4 to 4.55 (if it is below 4.55), then connect it to internet modem via cable/wireless then go to network settings, insert 2 DNS servers (108.61.128.158 and 165.227.83.145), after that go to settings/user guides then it is all set for now. Your Ps4 will be able to install fpkgs, run them and do much as normal ps4 can do but go online.