is it safe for babies to be exposed to chlorinated water (free chlorine concentration of 1ppm) in swimming pools? eg small splashes of water get on their face, and potentially into their mouths if they lick the water on their gums.

Should be fine. Baby swimming lessons start at 3 month old and the swim coaches submerge and let them dive underwater. Babies might take some chlorinated water into their mouth but it should be fine. Unless the water gets into their lungs, then having them splash about in the pool is safe.