The landlord already has a qualified tenant (you), so adding his name as a co-tenant benefits the landlord because now two individuals are responsible for the lease instead of just one, even if one has poor credit.
Assuming the SO doesn't have any particularly abominable personality traits (excessively loud or rude, etc.), three or four nights a week is perfectly acceptable. When you're talking five to seven nights a week, the roommate and the SO might as well make plans to get a place of their own.
A legally binding agreement with your roommate, which is carefully drawn out to eliminate problems in the future, is signed between the tenants and has nothing to do with the property owner. An agreement should include your basic details. For example, your name, permanent address, and workplace details.
Do Not Use Each Other's Things Without Asking. Not using each other's things without asking is one of the more obvious roommate rules. While some people are more casual about sharing, others are not. You have to learn what kind of person your roommate is and then act ingly.
You need to discuss this with her directly, not in a passive-aggressive way. Try to establish some rules like how often he can come over, how long he can stay, whether he has to stay in her room or in the common areas, etc.
It's not rude in itself. However, it's polite to offer to cook for them when you're already cooking anyway. Depending on your living arrangements, it can often make sense for one roommate to cook for the others, as long as they pull their weight in other ways.
There's no hard and fast rule about how often a roommate should have a guest. It's really dependent on what your needs are, and how often you're willing to put up with an extra human in your space. Perhaps weekends are fine, but you prefer not to have a disturbance on work or school nights.
3-4 times a week is completely normal IMO. Stop being awkward, if you're busy just politely tell him so, i'm sure he can entertain himself for 5 minutes-if he's over 3-4 times a week i'm sure he's comfortable enough to sit on his own.
Sample rules could include the following: A limit on the number of nights per week that a significant other can come over or sleep over. There's no set standard for how often a roommate should have a guest, so this could mean no weeknight sleepovers or a weekly cap, whatever you're both comfortable with.