Helldivers on PlayStation (PS4, PS3, VITA and PS TV) comes with full Cross-Save, Cross-buy and Cross-Chat. If for example you buy Helldivers for PS4, the game will automatically appear available for download on PS Vita. This works with any combination between the PS4, PS3 and PS VITA.
There is no cross-play, cross-play or cross-save between PC and PlayStation. You cannot transfer progress from PlayStation to PC, or vice versa.
However, both PC and PlayStation players will contribute to the same Galactic Campaign. There’s a nice post here by one of the Rocket League Devs explaining why cross-play is tricky.
You are not entitled to a free copy on Steam if you purchase Helldivers on PlayStation, or vice versa.