In 2v2 mode (Magma Chamber), the opponent moves in to fight my ally at a battlefield they control. Can I play Rengar, Trophy Hunter as a reaction to help defend my ally?

No — Rengar can't be played to that battlefield to help your ally.

Combat can only ever occur between units controlled by exactly two players (Rule 462), and a battlefield with a Staged Combat or Combat in Progress is an invalid destination for a unit controlled by anyone who isn't already a participant — by any means, including Ambush (Rule 462.2). Once the opponent's unit moves in against your teammate's unit, those two players are the combatants; you're a third player, so Rengar has no legal landing spot there. Rengar's expanded Ambush permission ("even if you don't have units there") only widens which battlefields are normally valid — it doesn't override the multi-player combat restriction, and if an effect forced a unit there anyway it would be played to your Base instead (Rule 462.2.a).

Note that a "friendly/teammate" designation doesn't change this — combat still counts distinct players, and your teammate's Defenders don't become yours. You can still play the Rengar itself during the turn (just to your Base or a battlefield you legally control), and you're free to help your ally with Reaction spells/abilities, since teammates can be invited to play cards with priority (Rule 489.8.a).