Not if you don't care that it will be much less of a system. Even the PS3 was designed to play online. Most but not all PS3 games are singler player when not online.
It costs $49.99 in a year to play Sony's PS4 online.
Yes, one must have a PlayStation card to play the PS4 online.
A person will not be able to hack the PS4 and then be able to play online for free. The games will need to be purchased as will the PlaystationPlus, which allows people to play online.
Yes, you must buy a PSPlus membership to play online games on the PS4.
No, if ps3 could play online with ps4 users evryone would just buy the cheaper ps3. That would cause sony to lose money which they do not want at all.
No. It is not possible for a PS3 version of a game that is also offered as a PS4 game title to play against each other. They can not play because the games are different software and whether they are both on the Playstation Network does not matter because the games are not compatible
You don't have to pay for online gaming, unlike the PS4 - you don't need PS+ to be able to play it online.
can you play destiny on the ps3 and play with a friend that has destiny for the ps4
The PS3 will not be able to play the PS4. They both are on the Playstation Network (PSN) and Playstation Plus will work for both of them as it does for the PS Vita and PS3
I think you're meaning PSPlus, and no PSPlus will not be free you will have to buy a PSPlus membership to play online.
connect your ps4 to your pc or monitor
No you will not be able to play the games either way. Systems changes on the PS4 allow them more design capability for games and many titles will be released in a downgraded PS3 version. You still will have to have a PS4 to play PS4 games and a PS3 to play PS3 games.