Removing HCl from water
1) Do NOT heat the solution, if you want chlorine out. Electrolysis of hot $\ce{NaCl}$ solution produces $\ce{NaClO3}$, then $\ce{NaClO4}$, not chlorine. You apparantly don't want this.

2) traditionally, in such setups some barrier between cathode and anode spaces is used. The easiest one would be unglazed ceramic pot (with no holes and no direct contact of anode and cathode solutions), though I'm not sure if it will work with chlorine ions. It is recommended to perform electrolisys of $\ce{MgSO4}$ solution first. In this case chlorine ions would migrate from cathode space. With barrier introduced you may expect chlorine to evolve from anode space and sodium hydroxide to accumulate in cathode space.

3) do NOT blow air atop sodium hydroxide solution. It reacts with $\ce{CO2}$ from air.