Hello Caro and welcome to the chat page.
If you are looking for long-term accommodation rather than just for a holiday it is best to arrange that while you are on the island. You will be able to meet the landlords, view the properties and negotiate the rent in person over a coffee.
The same goes for renting a shop. These are rarely advertised, relying on word of mouth and personal contact.
Perhaps you should spend some time on the island talking to people to find out what is available. Symi Visitor Accommodation should be able to help you with somewhere to stay while you look round. You can email them at:
symi-vis@otenet.grIf you intend opening a shop for the tourist season you will have to be quick!
Good luck with your plans.