Yes, they sneeze for the same reasons people do.
Badgers are the wildlife reservoir for Mycobacterium bovis in the UK; the badgers carry the bacteria in their respiratory tracts and sneeze/cough/hack the bacteria over the cow's food/water/pasture. When the cows come by and inhale over the bacteria, the TB bacteria are pulled into the cow's lungs and create an infection.
There are Eurasian badgers, hog badgers, American badgers, ferret badgers, honey badgers, and stink badgers. I'm guessing that your question was, "What kinds of badgers are there?"
coyotes eat badgers
yes, badgers are mammals
Badgers can swim
badgers do have tails.
All badgers are known to swim, therefore, your answer is yes.
If you sneeze on a Tuesday, you will kiss a stranger. The whole rhyme goes: If you sneeze on Monday, you sneeze for danger; Sneeze on a Tuesday, kiss a stranger; Sneeze on a Wednesday, sneeze for a letter; Sneeze on a Thursday, something better; Sneeze on a Friday, sneeze for sorrow; Sneeze on a Saturday, see your sweetheart to-morrow.
Yes.
badgers
Because when you sneeze the sound you make is "SNEEZE!" ^No, it really isn't. I've not heard one person say "SNEEZE" when they sneeze, ever in my life. I've heard people say "Achoo", "Atishoo" and other ones, but never "SNEEZE".
No. Wombats are never called badgers. They look completely different, and there are no badgers in Australia.