Hearing: This is where the judge actually sees you and listens to arguments (these are called “oral arguments”) you make about a motion. In some jurisdictions, a court will not rule on a motion you make without a hearing, but some courts do not require an actual hearing, and in some jurisdictions you rarely see the judge before trial.
Hearsay: An out of court statement offered for the truth of whatever was said. For example, if you testified that “Mr. Smith said the dog was white,” this would be hearsay if you wanted the jury to use the statement as proof that the dog was white. You must get someone to show up and testify in court that the dog was white. Or in the debt case context, suppose the company wants to prove that you owed Discover some money—they must either use the business records exception (see video: Business Records Exception) or have someone from Discover testify. It would be hearsay to claim that you owed them money because Discover sold them the debt.
Note that to be hearsay the evidence must be offered to prove the truth of what was said. To go back to Mr. Smith and the dog, you could testify that “Mr. Smith said the dog was white” if you were trying to prove that you believed the dog was white, or why you believed the dog was white, or that Mr. Smith was lying. Testimony can be permitted for certain reasons but not others, and you must ask the court to limit the use of the testimony if you want to keep it from hurting you. To do this, you ask the court for a “limiting instruction” to the jury telling them how they can use the testimony, and this can sometimes be very important. For video, go to Hearsay, As Close to a Silver Bullet as You’re Going to Get.
Hostile witness: A witness whose loyalties are with the other side or who is uncooperative. The judge will typically let you cross-examine such a witness even if you called him for your side, and you will be permitted to ask leading questions, which are normally not allowed in direct examination.