What everyone is trying to say is. For a bowl that small you NEED
to change the water daily. Fish produce a toxin called Ammonia. live plants help filter it out but letting it build up can harm and kill your fish. if you want another alternative, buy a 5 -10 gal tank and divide
it. This way you can buy a filter and a heater to give them the water quality they need.
Filters do not take away the need to continue water changes, which must still be done just not as frequently. Bettas need warmer water, you will either need to keep the entire room heated (to the point that the bowl water is KEPT
at the appropriate temp) if you dot have a tank heater, or buy a small heater for EACH bowl/tank. (granted a divided tank that allows water to flow through all partions only needs one heater.)
Bettas DO change colour, but what you have described is stress not a colour change. EG: when the lights on my tanks are OFF the fish show their full colours, when the lights come on they show a duller colour until they realise whats happened. when one fish intimidates another it can result in the same thing, the stressed fish becoming a dull or light colour, vibrant long stripes and clamped fins.
I see that your male is in sight of the female, yes its ok but sometimes this can stress fish.