Ps3 – Where can players find other players to team up against organized squads

You can find them on the PlayStation website listed under Games and doing some filtering on demos.

The current link is http://us.playstation.com/ps-products/BrowseGames?console=ps3&downloadableContent=GameDemos&beginsWith=Any

The problem is, these are for the US. Your profile shows Poland (might try http://pl.playstation.com/ps3/games/ to see if you can find Demos listed there), so I assume there may be some differences in what is available for your region. The other problem is, this link will likely end up changing at some point and time, so this isn't a real helpful answer and/or question.

I'm not 100% sure about the in-game chat, because I infrequently use it. However, I'm sure that you can use secondary chat channels (ie, Xbox Live Party Chat) while you are playing Hardcore Team Deathmatch, and that you can talk on them even while you are waiting to respawn.

This is different from Modern Warfare 2, where your chat options were limited. A spokesperson for Infinity Ward said:

“The only place where Party Chat should be blocked is Search & Destroy, and won’t be blocked for modes like Dom[ination].”

I would test the in-game chat channel, but I'm going to go ahead and say that it's highly likely that it works regardless of your current state.

If you're playing on PC, and you want to communicate always, you might look into Ventrilo or TeamSpeak, both are options that the game itself has little control over and the both integrate well with FPS games.