No, it is completely inappropriate. Giving your mother any form of erotic content is not only disrespectful but also goes against moral and ethical norms. Family relationships are based on love, respect, and appropriate boundaries.
It could be that the cat has some sort of skin condition. Maybe it has excessive oil production or there could be an underlying allergy that is causing its skin to be moist. Another possibility is that the cat has been in a humid environment.
Well, it depends on the context. In a private, consensual, and adult - only environment like some forms of erotica literature within a very specific and legal adult - oriented market, it might be considered acceptable. But in general, mainstream society frowns upon it because it can make others uncomfortable and may not align with family - friendly values.
Definitely not. This kind of content violates the norms of good taste and can be offensive to many people. We should focus on positive, healthy and respectful forms of literature and communication.
Regular grooming is key. Brushing its fur not only helps to keep it clean but also spreads the natural oils in its coat which can make it more water - resistant. If it goes outside often, consider getting it a raincoat or some sort of protective gear. And when it comes inside, use a hair dryer on a low, warm setting to dry it off gently.