Aw. Hope you did not give him a typical female name hahaha. It's great if you can get a cat from someone you know - I always did the same. Kittens are sooo cute, too! It's just that I did not feel like I was the right person for a kitten, since I live alone and I work 40 hours a week.
It's great that the kitten was able to take the kids' minds off the passing of the dog. It's always such a hard time when pets pass away - I feel like they're part of the family after all. It was also why I decided to get a new cat. Not to replace the old one, but primarily so that I wouldn't have return to an empty house every day. It made me feel pretty sad for weeks / months.
Actually male cats tend to be more loving and playful than female cats by the way! Plus, if you want to get it neutered, it's also cheaper (only around € 90 here).

Talking about getting them neutered - I remember my cat start spraying urine / marking at around 9 - 10 months, as well as continuously yelling very loudly. 3 or 4 weeks after he started acting like this, I got him neutered. This made everything stop right after the procedure, in case it may happen with your kitten as well and you wish to do something about it... haha.