'Pick up' can mean a few things. It usually means to take something from somewhere low, or to collect something from somewhere:
Pick up those clothes from the floor! Can you pick up a bottle of milk from the supermarket on your way home?
'Pick up' can also mean to receive, in the context of radio signals, or other communications:
I can only just pick up that new radio station in town.
'Pick up' cannot be generally interchanged with either of your other examples.
There is not much difference between 'pick' and 'pick out'. 'out' in phrasal verbs generally gives an idea of 'thoroughly'. If you pick something out, it means you deliberate more about your selection. So, they are interchangeable, but 'pick out' has an extra implied meaning of 'more consideration and thought'.
You can pick one flavour of icecream. / I'll have the Apricot Ripple.
I need to pick out a new dress. I like the white one, but it will be hard to keep clean. The green one is nice, but I don't think the colour goes with my skin. The short one is a bit too revealing.
'Pick out' can also mean to distinguish. We are so high up, that I can't even pick out my house from here.