Tips On Taking Care Of A Cockapoo Mutt?

I come home from college and my dad surprises me with a 6-week old cockapoo to take care of for the summer. I’ve never heard of a cockapoo mix until now. My dad said that he bought him from a friend of a friend, and he hasn’t been vaccinated yet. I had a labrador pup when I was younger, but had to give him away because of the house owner, so I don’t have a lot of experience taking care of a dog, but I’m determined to give this cockapoo a lot of love and care.
I read somewhere that since it’s a mutt (and possibly the product of a puppy mill, don’t really know who this friend of a friend of my dad’s is, but he paid them $100) that it’s more prone to health problems, but just because of that doesn’t mean that we’re going to abandon him! Just to be prepared though, what kind of health problems, if any, do cockapoos usually come across?
Basically what I want to know is:
-What good quality brand of food should I feed him?
-How do I get him to stop chewing and biting the carpet/couch/slippers?
-What kind of treats should I use to train him with?
-Is it worth it getting puppy insurance?
-How often should I bathe him?
-What kind of training methods can I use to get him to get along with my cousin’s 5-year-old chihuahua/jack terrier who seems to have a dominance problem?
-How do I get him to stop crying/get used to family members leaving the room?
Thanks in advanced!