Tank/Feeding/Water/Sick questions

I have had my betta for a couple months now and recently got a new one gallon tank with a filter. I just did a 50% water for the first time with this tank and now he is swimming around like crazy and hanging out mostly at the top of the tank. He hasnt eaten, and i got a glimpse of him and it looks like he has a tiny white patch near his gills. I dont know if it is a disease or just a coloration i didnt notice before. Also Im wondering if anyone knows how often you need to change the filter? Thanks in advanced!