[targonrotts]

first, check if your homeowners or your area of new home has any rottweiler restrictions.
then for your issues...
1. cat. a puppy can be brought up with a cat if socialized right. an adult rescue who had cats can also work out with proper introductions and socialization.
2.work hours. i have done it, as i also live alone. it's not impossible but harder. try to come home for lunch, get a pet sitter or walker, meet your new neighbor. yes, it is easier with an adult or older pup than a young pup. it is harder to housebreak and train if too young. right now i am on lunch break, came home to let my 4 dogs out.
3. no, get one dog at a time. 2 tend to bond with each other instead of you and work is double to train and socialize. when older and trained, then if you can handle it, it may be a thought. opposite sex is best.
4. add on. when you are with your dog, spend lots of time with him, train and socialize! exercise makes a less destructive dog.

welcome to the forums, you are getting some good advice here!