Any rooster breed can be friendly. It just depends on how much effort you put into getting to know him. Here is an infographic with some good tips - http://www.poultrydvm.com/featured-infographic/gentling-roosters
It sounds like it could be a number of things...have you tried the chicken symptom checker tool to help rule out the possibilities? http://www.poultrydvm.com/views/symptoms.php
Yes you can keep them together. Just keep in mind that ducks are lot messier and so you will need to design your run with good drainage, and an area so chickens can stay dry if they want to. Always need to watch to make sure they don't fight.
It could be a number of things. Have you tried using the chicken symptom checker tool to get an idea of the possibilities? http://www.poultrydvm.com/views/symptoms.php
It might be a better idea to leave that to the professionals who know what to look for and what tests to order. Most state labs have deals where it's insanely cheap to do yourself. Here is an infographic on how to do it -...
As long as your run and coop are predator proof, I wouldn't worry too much. Here is a good infographic with tips on how to predator proof - http://www.poultrydvm.com/featured-infographic/tips-for-protecting-poultry-from-predators
It depends on whats wrong with him. Each type of antibiotic is targeted to kill certain bacteria. In order to determine the correct antibiotic your vet needs to have a good idea what bacteria is causing it. Here is a chicken symptom checker tool which might help you narrow down the possibilities...
Going to the vet isn't actually that expensive. It's way cheaper then bringing a dog or a cat (if you go to a small animal vet who sees chickens). The exotic vet is more expensive. Here is a directory of all the types of vets who see chickens - http://www.poultrydvm.com/poultry-vets.php
Please bring her to see a vet. Even if you can get her to pass the egg, there is an underlying issue going on that caused it which needs to be addressed. Here is a directory of vets who see chickens - http://www.poultrydvm.com/poultry-vets.php
You could try using the poultry predator identifier tool - http://www.poultrydvm.com/predator-identifier.php but my suggestion would be to predator proof your run if you decide to continue keeping chickens. Here is a good infographic about how to do that -...
I think it has to be a certain depth or angle away. Here is a good infographic with details on this info - http://www.poultrydvm.com/featured-infographic/tips-for-protecting-poultry-from-predators