Installing a Heavy Sliding Barn Door into Metal Studs
I think it'll hold, but I'd have done a couple things differently. 


A taller board would've reduced the tension on your fasteners and the rotational torque on the board. I'd have gone with a 2x6 or a 5/4x6 board, or even a 1x6 if thickness is an issue. As it is you might see some gapping along the top as things flex.
Fasteners nearer the top would do the same. When you install your additional screws, put them 3/4" down. That's where most of the pullout force occurs. Picture a hinge running along the bottom of your board. If there's room, put both additional screws above the toggle bolts.


Regarding your questions...


Again, it'll hold. Worst case you get some bulging from the stud flange flexing. If you see that, make improvements. 
Your lag screws will penetrate the studs fine. I assume that you'll pilot the wood and steel appropriately, which you certainly should. For 1/4" lags I'd pilot 5/32". For 5/16" lags, 3/16".