Is it permissible to sell a shop that I rented without referring to the owner, and am I entitled to dispose of it by renting it to someone else for a large sum of money?

As long as a person possesses the usufruct of a shop through a valid lease and a lawful contract, there is no impediment to vacating it for another person in exchange for money, or leasing it to him for the same rent as the initial lease or more, according to the agreement. This is called selling the vacating of the shop, or the shop's 'khalu', or selling the key. There is no need to refer back to the first tenant as long as the buyer will use the shop for the same purpose the original tenant used it for, or for a purpose that is less harmful.