1) You are based on your apperance. Always.
Hell yeah. To take another example, show up in fatigue and T-shirt for a job interview, and show up in suit for another - see what happens. We're not talking huge reaction, here ; but some amount of judgement, definitely.
2) I can see wearing armor in town at times. But constantly dressed like the guy from Assassins Creed? If your doing something, why not! But if you are just walking around town, I agree with Kaziurra, it should be penalized.
Again, yes. I used the very same example as your op many times. The guards
at least should know me for DB and mightily dislike me. Other types of armour, given the situation... Dragon attack might spur the citizen to like you better so you'd help them, something like that.
In any case, on the question of realism, think of it like this : random guy wearing full body combat bullet-proof suit, holding a P90 : do you wave and say hi ? Granted, warriors are common on Tamriel ; doesn't mean the basic farmer doesn't view them as trouble.
This is about making unarmoured clothes actually
matter. I'd love to have to dress up according to situation.