I have no idea if he became a doctor or not but I can confirm he and Kacey are still together, or at least were as of a few months ago.
As for the other supposed rumors (the McFlurry thing, no sex thing, his fan fiction sending Kacey into a rage thing, etc), I have zero idea. They are plausible based on their personality types (Kacey could be overbearing and Liquid was beyond pussywhipped), but plausible doesn't mean it happened. The only source for it was an anonymous person on 8chan. Liquid's brother hated their relationship and was known to post on 8chan, so it could be more bullshit from him. While Kacey could be overbearing, she never seemed to be that psychotic in my interactions with her (she was more an attention whore than anything). So I doubt they were true, or they are highly exaggerated based on true stories (i.e. maybe Kacey was sick one night and wanted a McFlurry so Liquid got her one to be nice and Liquid's brother turned this into being a regular occurrence where she whined until she got one every night)