If both flights are on the same booking, and if you have your bags checked through to your final destination, then yes; otherwise no. Also depends on the airline - some of the budget airlines like Ryanair operate on point-to-point basis, ie. they don't do connections. Best to ask the airline you're first flying with, or just ask when you're checking in.

Well your luggage will go to your final destination as shown on the ticket, just make sure you can spell it so that you recognise it and get on the right plane.

if you bought the flight as one ticket and your transferring in the same airport then your luggage will be forwarded.

Probably - ask at check in to be sure.

No, it will go to Toulouse instead