I'm 5'5 what size should I buy?

Try medium-sized given your height, Also it depends on whether or not you like a snug or loose fit. It's all about your preference.

My son is 15 years old and measures five foot seven. What size should I get him?

Medium. I am 6' and wear the large, which isn't exactly snug. Medium should be perfect.

Are these pre-shrunk?

These FreshIQ t-shirts are not pre-shrunk. If you apply any heat to these when washing or drying they will shrink. I recommend looking into or buying the Hanes "X-TEMP" t-shirts if you are concerned about shrinkage. The X-TEMP versions from Hanes can withstand "extreme temperatures". Pun intended.

Do these shirts shrink in the dryer?

Washed in regular warm or cold water you shouldn't expect any shrinkage other than the natural tightening of the material the first wash. I've tried many brands of traditional white T-shirts or undershirts and find that these fit true to size, are comfortable and are a brighter white cotton than many.