Think you need to give a few more details here.
Obviously BBC iPlayer, ITV Hub, and whatever the latest Channel 4 and Channel Five apps are called should run on Android. As will Sky Player, if you have a Sky subscription. And Netflix (if you have a Netflix subscription). And Amazon Video, and Google video. And of course, Kodi opens up the world to you if you have a decent internet connection.
Does what USB stick work on a laptop? Any USB stick, or a particular one that you have in mind? If the laptop supports USB, and I've never seen one that doesn't, then yes, the laptop will almost certainly recognise the USB stick when you plug it in. Whether it can do anything with whatever material you have put on it is down to what kind of material this is, and in what format it is recorded.
Are you planning on using the Android TV box to source material from (say) the internet, then save it in (say) MPEG format to the USB stick, then connect the USB stick to your laptop to watch this material? If so, then yes, this should all work as long as
(1) you have links to one or more sites that will allow you to source online videos, and download them
(2) you have software on your laptop which is capable of playing back the material you have downloaded.
Seeing as Youtube - I think - allows you to download the videos you can watch on it (and if Youtube doesn't do it itself, I'm sure you'll be able to find some third-party software that will do it for you), and seeing as Windows Media Player is pretty adept at playing back most formats of video, I don't think you'll have much problem.
Of course, whether Youtube has such obscure programmes as Lard, Pinky and The Brain

I don't know. But you might find them somewhere.
The Kodi app will give you access to those paid sports channels you refer to - and most Android TV boxes come with some flavour of Kodi (or XBMC) pre-installed. But you'll then have to link to the channels yourself which provide these free sports channels. There's plenty to choose from though. Google is your friend....
No, you don't need a dish (satellite dish I presume). You do need internet connection though...