I would certainly say that BBC1 was a 'television station', but no, if it was showing a uninteresting programme (God forbid), I wouldn't say 'what's on the other station'. I suppose the distinction is between BBC1 as an institution, in which case 'station' seems appropriate, and the procession of stuff that appears on the screen, in which case 'channel' suits the purpose.

And yes, 'side' is probably the most frequently use used colloquialism. "What's on the other side?"... a fundamentally existential question to ask about so trivial a matter. I guess it worked better when there were only three sides to choose from, which is as far back as I can remember. These days, to imply 'sides' would be to conjour up images of a monstrous Lovecraftian dodecatriskahectahedron, hanging ominously in netherspace like something from a Grant Morrison comic.