physical chemistry - Why does liquid water form when we exhale on a mirror?

In the descriptions below, I always assume external pressure to be constant at 1 atm, the condition where daily observations are made.

1) When I exhale on a mirror, liquid water forms on the mirror. That's condensation. Obviously, the temperature of mirror must be < 100 °C, so water vapor condensing on mirror makes sense. However, in that case why do we have water vapor in our breath when our body temperature is also < 100 °C in the first place?

2) One reason for (1) may be like 'water vapors in air is in equilibrium with liquid water', so some water vapors can exist although T < 100 °C. If this is correct, based on this reasoning, then why doesn't ice exist at T > 0 °C? [p = 1 atm only]

3) If liquid water can evaporate into gas at T < 100 °C, then why doesn't ice turn into liquid at T < 0 °C? (I never use the term 'melt' here, just like evaporate≠boil) (both have hydrogen bonds, intermolecular forces should be the same?)

4) When I exhale on a wall, no water droplets form. Why do water droplets form on mirror but not on wall (just an example)? The mirror must have the same temperature as that of the wall, both of them must have achieved thermal equilibrium with their surroundings a long time ago.