I recently bought rebuild 3 and have started my adventure. I claimed many buildings, including, a market, office, and GamePop. I'm sure there are many like these too. Do these building do anything or can they be converted into farms and apartments. I know banks and police stations actually do something but do these?
No, they do not. Depending on the amount of Resources you have, and your needs, you may want to convert them to something more useful, or not claim them at all.
If you have Survivors who have the "Redecorator" talent, they will occasionally convert useless buildings into useful ones - it's nice to wake up one day and find that your useless Cafe is now a Bar or Workshop. In that case, you may find it useful to annex useless buildings and let your Redecorators convert them in their spare time.