NSA sex is not normal in my poly world, but for others it may be.
As for the other issues.
Speak up be firm about your needs for time alone for more than the short time you are getting. If he can't meet your needs, which to me are not outrageous, then I would end the relationship. You deserve to get your needs met.
Situations like this is why I dislike the primary secondary relationship model.
40 yo straight female
Married in the eyes of the government to Butch since 2001...
Murf my monogamous second husband has been with me since May of 2012.
In a V relationship with an average 60/40 split of time. Only due to Murf's and Butch's crappy work schedules.