Welcome! Glad that you are asking questions before you consider adopting a dog.
Sounds like you have put in alot of thought..and I think you would make a good dog owner.
An adult dog will be fine alone for the hours you work. Please do not think of getting a puppy, and forget about getting two puppies at the same time.
They will spend their time alone, and will bond to one another. They will need an extra ordinary amount of time to train and bond with two puppies..almost impossible for someone that works full time and lives alone.
I would suggest you get in touch with your local Rottweiler rescue...and look for a young, or middle aged dog to adopt. A dog that does well with cats. Most rescues have dogs living in foster homes and can tell you the info you need to know before adopting.
Rottweilers and cats do fine in most homes...as long as the cat has a good exit plan and a room that the dog cannot bother the cat in.
I would also find out if your home owners insurance will allow you to have a Rottweiler...many companies do not.
If you do get a nice dog, then get the dog enrolled into obedience classes, and when it's all trained an settled in your home (a year or two), then think of adding an opposite sex dog to your home. Opposite sexes do best in most homes.
Gina