Hi,
Buying an unlocked smartphone just means that you can use any SIM card in your phone, or in other words the phone isn't restricted to work with only one carrier, that's all. You will only "activate" the connectivity of the phone to broad networks, the firmware features like wifi are independent of the activation, to have those features working you only need to charge your phone and turn it on.
Then, if you buy this type of device you will have available all the features that come with it (music, wifi, organizers and more..) however, if you don't use a SIM card you won't get access to data, which is the element that allows using apps like instagram, facebook, twitter an more, you won't be able to check your email or browse the web either.
Hope that helps!