for #1 I'd suspect you've something wired wrong or a bad left socket/bulb - probably the 'hazard' function is working by activating the parking light filaments rather than the turn filaments, so that doesn't necessarily mean the bulb or both wires to the light are good
for #2, the front parking lights are just that, parking lights, they are only on with the first position of the switch, the rear "parking lights" are tail lights, on in either the
park position or
drive position .... if you want the parking lights to act as
running lights [a modern thing not found on the old vehicles], see
this tech tipBill