Per CalTopo, the distance from the trailhead to the top of Old Army pass is 7.6 miles, and another 2 miles to the summit of Mt. Langley, so approx. 19 miles round trip. Shorter than Whitney by 2 to 3 miles, and less elevation gain. So, if you know your approx. time up Whitney, you could subtract an hour (or more), and be very close. A "typical" time for Mt. Whitney might be 16 hours, so perhaps 15 hours for Langley.
There is drainage near the top of Old Army Pass (snow melt, I guess), but have no idea if it would be running at this time. Lake 4 should have lots of water, with easy access from the west shore, and is at the base of the climb up to the pass.
Not sure why you would want to return via New Army. Adds a mile (or so), requires more elevation gain, and will take more distance to get back to water. This means you will use a bit more time going back. The view from New Army is really nice, and the boulder field going down is quire remarkable, but would not be worth the extra effort for me.

Check out CalTopo: https://caltopo.com/map.html#ll=36.48052,-118.21195&z=14&b=mbt
If you "right click" you have the option to measure distance, and the tool will track the trail, so easy to use with fairly accurate distance.

Enjoy, it's a lovely hike.