The betta in the picture is a female. Her ventrals are not as thick as a Plakat males would be.
The white patch could be several things, but the top 2 that come to mind but would have to be cultured at a lab would be Columnaris or fish TB. I'd be very careful for the time being as far as sticking your hands in the tank. I wish Basement Betta's would have replied, as she knows someone that has dealt with TB and there is a med that you feed to them. It starts with an M (maybe she will see this and post). For Colunmaris...that is a toughy...as an experienced breeder, you'd dab H2O2 directly onto the spot, but as a pet owner, if your NOT careful, you could get it into the gills and it WOULD kill her. I suggest researching both that are listed, and if Basement Bettas see this, I hope she replies. She has done a lot of research and is very knowledgeable on this....I've often asked her why she didn't go into Marine Biology :)