Well those two things you say the Sky app doesn't do.....
........it does.
Erm....yes you can!!with this app you can select each channel to be selected or not. like u can have MTV on but have MTV base off. u can't do this with sky. also for me if I use search function it only gives me results for today.
Erm....yes you can!!
There is a Favourites option, second one along between guide and search, that you can set up with various channels of your choice and then once done you can use that to just see the channels you want.