How to create objects dynamically by passing type in c#?

The normal approach is using reflection to enumerate the available types and map them to the requested type. But instead of doing this manually, you should use a dependency container like Unity or MEF.

Where does the type string comes from in the first code snippet?

functions["PRODUCTS"]();     // Executes ProductsList() 

This has a very strong code smell. Using a discriminator is often a bad sign. Normally you can use inheritance. But for concrete advice you should show uas more of your code here.