Been trying to understand this question. Here is my reasoning:
1) True, because T is positive (105 + 273)K while ΔS should obviously be negative because the final entropy is lower than the initial entropy. We are after all going from water's gaseous state to its liquid state. There are fewer degrees of freedom in water's liquid state.
2) If there is an equilibrium between water vapor and water liquid, then by definition relative humidity is 100%. The air is saturated with water vapor to the point where it can't even hold the water vapor and water vapor exists in a dynamic equilibrium with liquid water. From Wikipedia:
Saturated air is really just air which contains water vapor in equilibrium with a liquid water source.
3) False, because ΔG, not ΔG°. ΔG for a system at equilibrium is always 0. ΔG° - not necessarily 0. So we have 0 = ΔG = ΔH - TΔS. This implies ΔH = TΔS.
4) True. For liquid water to boil, vapor pressure must equal atmospheric pressure. Similarly for water to condense, atmospheric pressure must equal vapor pressure. Also, vapor pressure is solely dependent on temperature of the pure liquid. The below statement is from UC Davis's ChemWiki. I would think that adding solute would change the vapor pressure (and yes it does, and it's discussed further down the page of the site).
Vapor pressures are dependent only on temperature and nothing else.
Taking into consideration that water boils at 100 degrees Celsius, we may conclude that at 105 degrees Celsius, the vapor pressure of liquid water is greater than 1 atm. And therefore, for this equilibrium to exist, both the vapor pressure of liquid water and the atmospheric pressure of gaseous water must be equal and thus greater than 1 atm.
5) This is true. This would make ΔG = 0 since ΔG = G(products) - G(reactants).