Will my milk supply dry out if I don't breastfeed routinely?

Yes. It will definitely dry out if you stop breastfeeding. How little breastfeeding you can do and still have milk is highly individual.
Yes. To produce milk for your baby you have to breastfeed freguently with baby having a good latch onto the breast. Some babies may not be able to latch on well if they have "tongue-tie". If you are having such a problem your pediatrician can refer you appropriately. Try to avoid supplementing with a bottle or pacifier that decreases subsequent nursing strength and stimulation of milk production.
Yes. Best food for your baby your milk produced by frequent nursing, not bottle supplements, not pacifiers. Baby's latch very important in order to stimulate milk production by you. Poor latch may also be due to" tongue-tie" your pediatrician can help you with that. Learning about breast feeding long before birth helps a lot.