I bought everything in the Flea Market and it didn't restock. Is this a glitch?
The Flea Market restocks approximately every 6-7 hours.
Why are items 1/2 price in the Sale category of the store but at the same time full price in another category of the store?
Those are actually two different "places" to purchase items. Think of it as separate showrooms (one for the regular store, and one in an "overstock" area). In order to get the sale price, you must go to the sale area.
What do the locks on store items mean?
The number on the locks tells you how many generations need to have owned the house before that item can be accessed. Once you have reached that generation, the lock will be removed. Please see this article for more information.