Does Scotland shops shut down for two weeks like some parts of Europe? If so, what weeks?
No, things will not be closed.
Back in the day, and up until the mid 1970s, many shops were closed in Glasgow during the annual Glasgow Fair. (A two week period in July) This no longer happens. Scotland has become a lot more consumer oriented, with supermarkets and petrol stations open 24 hours, and most shops being open on Sunday. Smaller towns used to have an "early closing day," in which shops would close at noon or 1 p.m., and not open until the next day. The towns staggered their "days," so that if your town was closed, you could nip over to the next town or village to do your shopping.
There used to be a period between Christmas and Hogmanay, called the "Daft Days," during which most offices closed, and factories shut down. However, you will still find not too many shops open on January 1st. and January 2nd. Mostly corner groceries and newsagents open on the 1st., and the larger stores will reopen with a skeleton staff on the 2nd. In 2019, Tesco, Asda, Sainsbury's and Morrisons will be open on January 1st., albeit with limited hours.
You need have no fear. Scotland is open for business!
No there's no summer shut down here! You may encounter Sunday closures if you travel to the Outer Hebrides as the Sabbath is observed more out there. It's certainly worth knowing about as even the petrol (gas) stations are closed.
Another thing to bear in mind about retail in Scotland is that shops are only allowed to sell alcohol between 10am and 10pm. Obviously this doesn't apply to licensed premises such as pubs, restaurants and hotels.