Congrats on the little mojave! I like the name too!
1. I take my snakes outside for photographs and a quick slither, but never too long and always supervised 110% of the time.
2. I have a cat and a dog. My dog is very well behaved and will leave the snakes alone. The cat does not listen. I try to keep them apart as much as possible. Dogs and cats both have a high prey drive (depending on the breed I suppose) so I would never trust either with my snakes. Dogs and snakes can both be unpredictable. Best to just keep them apart for their own safety.
3. The longest handling session I would do is about 30 minutes. Some snakes are comfortable with more, but usually the young ones get stressed a little more easily. As your snake gets older, you will notice it will calm down a lot more and just kinda "chill".