What does it mean when dough is referred to as "short"?
"Shortness" in dough refers to its tenderness, which is influenced by the amount of fat as well as sugar. If your quiche recipe calls for a short dough, it would be referring to a higher ratio of fat to flour since pastry for quiche typically doesn't include sugar.

Both fat and sugar minimize and break down gluten development which results in "short" protein strands and thus a more tender result.  As the fat is rubbed into the flour, glutenin (providing strength) and gliadin (providing elasticity) are coated with the fat which acts as a lubricant to keep the two from being able to link together forming gluten when liquid is added to the mix.

The higher the amount of fat in a dough the more tender it will be.  If you want a dough to be flaky then you'd leave the fat in larger particles which will blister to form flakes.  If you want a dough that will be moisture resistant to fillings (such as a quiche) then work that fat in finely so that it will be less likely to absorb moisture during and after baking.

Quiche crusts (and crusts for other custard based pies... pumpkin, sweet potato, custard, etc) should first be blind-baked for the crispest crust in the finished result.

As for "fixing" a pastry dough...it's usually easiest and best to simply start over.  Water is added a little at a time to avoid adding too much.  If too much water is used then more flour needs to be added but with the excessive flour and water then comes additional gluten.  If you get a pastry dough too wet, I would be inclined to rub some additional fat into flour and then add that to the first dough rather than just flour alone.  Too little shortening will really only be noticed after baking and that's going to be determined through how tough or tender the dough is.

Keep in mind that toughness also depends on the amount you've handled it.  Short doughs typically can't be handled too much because the higher amount of fat means that they will warm and get sticky.  It is best to refrigerate to firm up the fat rather than add flour as the flour simply dries it out.  The tender nature of the dough from sugar means that in some cases they can be impossible to roll out and transfer to a pan.  In this case they are usually put into the bottom of the pan and then patted out across the bottom and up the side.