Coughing while bottle feeding is not all that uncommon. But if she does it all the time, check her temps, and see if she may be in need of some treatment. If you have doubts , always err on the safe side and treat, It is not uncommon for calves to get inhalation or asperation pnuemonia from inhaling milk replacer.
As for the bad breath....I can't advise on that. Maybe some listerine? Kills 99.9 % of bad breath germs on contact? Just kidding.
As for the calf with the swelling. you can find out easily enuff if you are dealing with a birth defect an injury or another problem such as an infection... manipulate the area, if it is soft like and you can push your fingers into it. it is likely an infection, and you may chose to drain it, to be sure insert a large bore needle and try drawing some fluid out, if puss or watery blood comes out , drain and treat with penicillen, inject the penicillen around the injury after you have fushed it, and lastly your last flush should be a bit of penicillen inside of the cavity you just left.
If it is hard, you can still try needle withdraw to see what you have in there. and treat accourdingly.
If it is in an area around the teeth, check inside the mouth for swelling and puss area, it may have an object stuck inside the gum or teeth area as well.
I recently saw a calf that was born with a defective mouth, likely due to a broken jaw when it was born, and she is now 3 years old, but looks like a lumpy jaw.
Hope this helps....good luck! :cboy: