I have bicep pain, is it soreness, sprain or tendon tear?

Varying degrees. Think of the severities you listed as a continuum. - if you have bicep soreness following any increase in your normal level of activitiy, then you likely strained the muscle fibers. The pain associated will likely subside w/ a proper amount of conservative treatment (rice). If no improvement see a physician. A strain itself can be of varing degrees & in the most severe cases a "tear" may result.
Depends. I suggest you get in to see your physician who will take a medical history and do an examination. It could be any of the possibilities you mentioned as well as a number of things you didn't mention.