How many feedings can I skip without making my milk supply dry out?

1, 2. Not many. Your milk supply is determined by a simple demand and frequency of stimulation practice. If you skip feedings without pumping this signals to your body less demand, therefore less milk is made. Try to pump every 4 hours when you are away from your baby. See the CDC website for breast milk storage guidelines.
1. Breast feeding is based on a simple premise, demand and production. If you skip feeds your milk production will decrease.Also remember that a growing infant will require more volume of milk as he or she grows, for example, a 2 month old infant commonly will take up to 32 ounces of milk per day. Babies will typically, double thieir birth weight by 4 months of age and triple it by a year of age.
1. Skipping more than one feeding will likely cause engorged breasts and back-pressure in the milk glands, which can decrease milk production. Pumping the breasts at the time of the "skipped feeding" can empty the breasts and maintain milk production.
0-1. I think you will have to pump and feed regularly to get to keep your brain signals and your milk supply going.