In a 2v2 team setting, are there still only 3 battlefields and the first player does not get to draw a card?

In a 2v2 (Magma Chamber) game, there are indeed 3 battlefields used, and the player going first does not draw a card during their first Draw Phase.

According to the rules for 2v2 (Magma Chamber):

• Battlefield Count: There are 3 battlefields in play (Rule 484.4).
• First Turn Process: The player going first does not draw a card during their first Draw Phase of the game (Rule 484.7).

Additionally, note that in 2v2, the player taking the first turn removes their battlefields from the game, and they are not used (Rule 484.5.b).