I would say one gallon per plant is enough for your reservoir.

Changing solutions can be very important but not critical to the success of your crops, failing to do so can reduce your productivity by almost 20%. You should switch between when the first and second flower clusters develop.

Yes, you can, but you may carry on soil born disease. Wash the roots with a 0.03% hydrogen peroxide solution to sterilize them as much as possible.

In an NFT system your tomatoes would most likely wilt quickly but it would take them 6-12 hours to actually die. It would be wise to have some sort of backup power system.

Those are my opinions, I hope they were helpful !

Here is a link that might be useful: Everything Hydroponics

Tomato plants can consume two - three gallons of water per day per plant. Mine did last summer. When my grow room hit 90 F, I had to add 1-2 gallons of water every 12 hours to my tomato plants. I would recommend at least 5 gallons to each tomato plant for your tank as you need enough water left over at the end of the day so that your nutrients are not too strong.

Switching from grow to bloom is more about the type of plant and how it is growing. I have had peppers that start to flower after the main stem splits, and then some that do not start to flower until it is almost fully grown. The best rule for me has been to wait until after most of the blooms are open, and you can see several fruits start to form. I also use Bloom to get a plant to bloom so that is another use. I also use Bloom on plants like pepper for their entire life as Grow contains too much nitrogen for peppers.

Tomato plants usually set a few flowers when the main branches split, and then may not set more for a while. Tomato plants in hydro can grow up to 10 feet tall. You will need to know how to prune the plants.

You can wash the dirt off of plants roots that were purchased from the store or nursery. As commented before doing so introduces bugs into your garden. I lost an entire garden one time doing this. It is best to grow from seed in sterile media like peat and then wash the peat off the roots and transplant into hydro. However, I have purchased plants and been successful.

The plants would likely be fine for several days, and here is why. If you are growing indoors under lights, the lights create the heat, the plants use more water the hotter it is. If you are growing outside, it would depend on the weather more than anything 2-3 days average.

Other things to consider when growing tomatoes are: how do you plan to support your plants.

James:
If this is a project where you are demonstrating how hydro works, 'simple is best' (unless someone is willing to bank-roll your efforts). NFT will cost several times more than a simpler method.

I'd recommend using the "static" approach. As tomato plants grow, their food and water demands grow also. Using static, you can offset the daily dry-out problem by placing your pots in a small pool of nutrient (or even plain water) and top watering using prepared nutrient solution. As they use up water by transpiration (what it's called when plants grow), there will be enough water available so they don't dry out. One or two dry-out days and they're goners!

As the plants mature, you can trim them back (plenty of online help available) and you'll produce the same or better results as if you were using NFT, which requires pumps and timers and lots of ancillary gear.

If it's a show-n-tell project, there's no reason to get too complicated, right?