1. Here is a link to a map for the old trail (which I descended earlier this week):

Old Trail

It's about a half mile long (and a half mile shorter than the main trail). But, the elevation gain is about 450 feet over that half mile which is not insignificant. (You can click on the elevation profile icon to see the gain.) My recommendation would be to take the main trail and take it easy warming up for the rest of the hike.

If you do decide to take the old trail it is easy to follow.

2. What has worked for me is to bring two one-liter bottles and a two-liter reservoir.

The one-liter waters are for filtered water, and the reservoir is for unfiltered water and is used with a filter to refill the one-liter bottles.

I'll start with 2 liters of water in the one liter bottles and an empty reservoir. Then I'll stop at Trailside Meadow (the creek is right off the trail there), filter enough water to refill/top off the one-liter bottles, and fill the reservoir.

At the summit I'll refill / top off the one-liter bottles with the water from the reservoir.

You could carry less and stop more frequently along the trail to refill. I don't like to stop so my only planned stop will be at Trailside Meadows to refill before hitting the switchbacks. I don't mind carrying 2 liters from the start, but you could definitely carry less and refill along the way.

The switchback water source was flowing well on Monday earlier this week.

However way you do it I would recommend carrying 4 liters for trail camp/switchbacks to the summit and back.

Don't forget to hydrate before the hike...I try to drink 4+ liters of water each day for 2 days before the hike.

3. On Monday I passed through Bighorn Meadow in the early afternoon on the way to spend the night at Outpost Camp and it was not a problem. But, based on other reports if you are passing through there in the early morning you may want to bring some lightweight water shoes. I like Steve C's suggestion to stash them and pick them up on the way back. This is the only area where I can imagine you would need water shoes.

4. You're starting as early as possible which is great. Check the weather forecast frequently up until the point you no longer have cell coverage and watch the weather while you're on the trail, as it can change quickly. On Monday it was sunny and cloudless at Trail Crest while I was descending, but by the time I was at Trail Camp dark clouds had rolled in.

Have a great hike!