HTC and Samsung are Android phones so whatever you can get on the Samsung (apart from their own rubbish apps) you can get on the HTC via the Play Store.
I have a Samsung on the Vodafone network and do not really come across problems with their service. If you can get internet, then you can get Utube etc.
As to the unlock bit, you will need to take that up with ASDA and see what their policy is. You might have to pay a few pounds to do it, it might already be unlocked or you might have to wait a certain period before being able to unlock it. Ask ASDA.
ASDA FAQ on locked phones.