1) Chlorine actually will react with according to the equation:
Cl2 + H2O → HCl + HClO
This is a disproportionation reaction whereby Chlorine is both oxidised ( 0 in Cl2 to 1- in HCl) and reduced ( 0 in Cl2 to 1+ in HClO).
This is rather a reaction than ordinary hydration. Thus, this happens relatively spontaneous. The Chlorine ions in HCl will ultimately becomes soluble in water, thus, chlorine will be soluble in water. Hope this answer your question.
2) As of my best understanding of Chemistry, chlorine gas is not reactive. However, as we have discussed earlier, chlorine will react with water to form HCl (hydrochloric acid) which is an ionic compounds. This enables HCl or some prefer to say chlorine to react readily with other ionic compounds as well as some organic substances.
The presence of water will greatly increases the reactivity of chlorine.