Is it possible to finish the game in leather armor (or possibly scale)?
Reason being I dont like the look of Elven or Dragon or glass.

Markarth guards armour is nice looking.
And yes, yes it is.

you can smith them up to be pretty good. i would say, yes you can. i don't know what kind of difficulties you an take though. on adept it is definetely possible. played with steelplate armor for a while(in the 40s) and you can't even smith it up to legendary.

I play on expert

I've finished it as a melee character wearing robes on expert, its very doable

Robes! Wow...how did you do that?

If you use enchanting and smithing combined, expert difficulty might even become too easy.