Do I Pay When all My Groups are Inactive or Archived?

No, you only pay for active groups. In other words, only active groups count towards your total groups, which is used to automatically put you into a specific plan. 

For example, say during the Spring season you had 25 groups, which put you on a paid plan that you paid each month during the Spring. If you make all of your groups inactive or archived for the Summer season, then you will be moved to the free plan (5 active groups or less).

Please note that on the free plan, text messaging capabilities don't work.