At two to three months, he'll need 80% feeders (crickets, phoenix worms, small butterworms) and 20% greens. He probably won't want many greens at this age. However, I would put greens in his viv with him and use collards, mustard, turnip greens. You can use some romain lettuce, just not much because that will give them more water than nurishment. About the pre packaged salad mix, it depends on what's in it. The only thing that head lettuce is good for is a beardie that is dehydrated. Head lettuce has no nutritional value at all, the romain and green, read lettuce are better, just not that much.
Not sure on the water, but I give my reptiles and tarantulas regular tap water all the time and have no issues. The quality of the water varies greatly from city to city anyways. Bottled or distilled water would probably be the safest bet, but tap water has worked fine for me.
As mentioned above, the salad mix would depend on what is in it. Check out http://www.beautifuldragons.503xtreme.com/Nutrition.html for a list of things that are good and bad for your beardie. I would recommend cutting back on the cucumbers quite a bit, as they have no nutrition to them and are almost complete water. They work well for helping to hydrate, but that can cause some runny poo, same as the head lettuce. Checking the chart out, Kale isn't a good thing to feed as the staple salad either. The greens mentioned by Beardie Parents are definitely the way to go.
You could give him just mustard greens only and he might be ok. However, I highly recommend you offer some variety, even if just once a week to keep him from getting "bored" of his greens and to add some other natural vitamins into his diet. Would you be happy eating spinach all day long every day of your life?
You could stick with just mustard greens and add a variety of veggies. If you are eating, say peas for dinner one night, wouldn't hurt to add a few to the dragons dish tomorrow. (just an example)