Gash where valve meets tire tube; How could this happen, and can I fix it? I'm fairly new to bicycling; apologies if this is a standard question but I couldn't figure out how to phrase it to search for it elsewhere.

I ride a KHS Urban-X with Kenda Kwest tires (just what it came with). I've gotten barely any use out of it since owning it, and it's been resting comfortably in the living room through the winter, so I decided today was a great day to get back on. 

So I unscrewed the back tire cap, and began to hand-pump air into the tire. All seemed to go well, and the tire held pressure fine, but when I removed the tire pump, the pin appeared to remain pushed down slightly, and air flowed back out of the tire. I looked, and this is what I saw:



Several narrow gashes that appear as if the rubbed was ripped, cut, or separated somehow.

Questions


Is this a common occurrence? Again, I've ridden on this bike very little and thus filled up the tires even less. We have no animals and no bugs around that I know of that would gnaw or chew on such material.
Is this fixable, or is my tube completely shot? It would seem to me that the latter is the case.
Is there anything I can do to prevent this in the future? I use a hand pump but am gentle; would a stand-up pump be a better choice? 
Do bike tires come with a standard warranty for cases like this, or do you know of any brands that do? If I have to purchase new tires, I'm going to purchase
Is there any kind of "off-season" maintenance that I should be performing on my bike that could prevent things like this?


Thanks in advance for any help you can give!
Most likely this is a result of riding the tire while the pressure is too low.  When you do that the tube tends to slide around in the tire and can get cut against the edge of the rim.

However, this could also be the result of using a hand pump, which, if you don't "buck" it against something or hold the head steady will move the stem back and forth rather violently.  A "floor pump" prevents this sort of damage (and also makes inflation much easier).

The tube is toast.  However, this is not a particularly expensive repair.  A new tube will run you $5-10, and replacing it is something you need to learn to do anyway.