Catch and Carry?

 
With no outs and the bases loaded, the batter hits a foul pop-up near the 3rd base dugout.
 
The 3rd baseman chases the foul ball and catches it with one foot on the ground in the dugout and one foot on the ground outside the dugout. After catching the foul pop-up, both feet then end up on the ground in the dugout.  The 3rd baseman then sees R3 standing 15 feet off of 3rd base, so the 3rd baseman exits the dugout, returns to live ball territory, throws to the shortstop, and R3 is tagged while off of 3rd base.
 
Is the batter out, R3 out, both out, neither out? Are there any base awards?
 
Call
In NF (and only NF), if a fielder has at least one foot in live ball territory and the other components of a legal catch are met, then it is a legal catch (NF Casebook 2.9.1c). The when a fielder carries a batted ball into dead ball territory with both feet, the ball is dead (NF 5-1-1i) and each runner is awarded one base (NF 8-3-3d).
 
In the situation below, in NF (and only NF), the catch is legal and the batter is out. The ball is dead when the third baseman had both feet in dead ball territory and all runners are awarded one base. R3 scores and R2 and R1 advance one base.