Is it possible to configurate a key that way it sends to all instances of the game while broadcasting is off?
Yes. You can use the Mapped Key Wizard to set up custom Hotkeys, which are active while Broadcasting Mode is off.

I´d love to run and cast with broadcasting turned off, because i think picking up loot would be a lot faster.
If Broadcasting Mode is off, you won't be able to run or aim very well in Diablo 3

Can I somehow setup a key that is rightklick and shift at once? (would that be allowed?)
Yes. Set up a "Key Re-Map" using the Mapped Key Wizard, give it a Hotkey for you to press, and tell it to press Shift+Mouse2. This is allowed.

Can I setup a key, that starts with client 1 and when i press it again it goes to client 2 and so on? (for round robin on skills) It would be amazing if the key had an internal cooldown so it restarded sending the command to client 1 after xxx seconds...
Yes. There is a Round-robin option in the Mapped Key Wizard. To auto reset after ___ seconds, then AFTER using the Mapped Key Wizard you can open up your Mapped Key's Advanced options and configure "Reset to Step 1 after ____ seconds"