The thing that works best is that you learn one position first and use a backing track to improvise. Be comfortable with the entire position before moving on to the next. If you don't do that and learn every position, the consequence will most likely be that you won't be able to make music from it but rather play it up and down ( which is really boring ofcourse ).
So work on one position and learn to fully use that before moving on to the next. Key isn't of any importance, but backing tracks in the key of C major or G major are useually often used to start with since those are low and mid on the guitar neck.
And in reply to your question, are these shapes movable ? Yes they are! For example if you have the shape of the first position in the key of G ( the lowest root is on the 3th fret low E string ) you can move it up to any other place on the guitar, for example to the key of C ( the same position/shape would then start on the 8th fret of the low E string ).
Some tips for improvising ( this is a copy/paste from another website which I find very true ):
• It's a good idea to stay mostly on the thinner strings, thick strings (low sounds) tend to get mushed up in the bass frequencies and not sound as good.
• Make sure you play a bit and then stop, play and then stop. If you play too long without a break it just gets boring and people will not understand what you are 'saying'. You can think of it as the play/rest approach if you like (one bar on, one bar off). While you are learning it is useful too - you get to stop and think about what you are doing next, and it sounds better - bonus!!
• Keep it simple. It will sound better.
• Often repeating an idea while the chords change sounds good.
• Explore - do not be afraid, the worst thing that can happen is that you play something that doesn't sound great!! So when practicing try and explore as much as you can.