I don't think there is a hard and fast rule regarding "how much", the
calories in juice count the same as any other.  I do believe that if you are
on a low card diet juice should be avoided since it is high in carbs.

When dieting I avoid juice altogether.  I found, for the most part juice
contains a higher calorie content by volume than I am interested in
consuming since the fiber has been extracted.  In stead I focus on the
actual fruits or veggies since they allow me to remain full longer.

a. If you are going to drink juice it can replace some of your water,
remember 1 c. tomato juice = 41 cal and water = 0 cal.
a. To answer the question regarding adding water one needs to understand why
you are consuming juice.  Adding water will simply allow you to reduce the
calories by volume, 1 c. water + 1 c. tomato juice will have 41 cal/2 c.
instead of tomato juice alone which is 41 cal/1 c.  This allows half as many
calories by volume in this example and will have the same nutritional values
as the 1 c. of  "full strength" tomato juice.
a. I don't see any reason why you couldn't store juice in an air tight
container...just refrigerate for food safety.

Store in refrigerator.  I think the shelf-life refrigerated is still
relatively short.

For longer storage, freeze it.  You could can it, but with veggie juices you
will need a pressure canner (fruit juices can be boiling-water-bath canned).
Canning requires cooking the juice, so you'll use that "fresh-squoze" taste
(and possibly some nutrients).

I'm not a food scientist, but it's possible that you'll lose some nutrients
with any juice that's been around for a while.

Anny

Not - but I often dilute my juice with water.

I drink about a cup a day.  I don't think I'd drink more than 2 cups
per day (too calorie dense).  There is proven benefit of drinking a
cup of juice per day (ie. orange juice and it's affect on lowering
blood pressure) but, like anything, too much of a good thing...

Gary Null and other anti-aging progams are proponents of drinking
juice, but in those cases is usually vegetable and fruit juices,
fresh/hand squeezed, and 'sipped slowly' during the day (not
'chugged').

Hand squeezing juice is too bothersome for me, but i try to drink as
natural a juice as I can find - avoid juices high in sugar
(glucose-fructose), choose ones high in pulp (fiber, and slows
digestion).  Tropicana and Minute Maid now have a couple of good
calorie and sugar reduced juices available.

No.  In fact, it's better from a blood sugar and calorie perspective.

I've heard that you can make it the night before for the following
day, but not store it any longer than that (but again, I'm not really
into juicing, so...)