A buzzard is a kind of bird, and in this example the phrase "ol' buzzard" (old buzzard) is probably just a reference to to Pa Forrester being old. In this example, Buck is saying that Pa Forrester has the most sense despite being so old.

Someone should correct me if I am wrong, but I think: '공부를 해야 해요' is more of a 'I should study.' and '공부를 해야 돼요' is more of 'I need to study. Hopefully you get more insight into this if I am incorrect.

I would reword this, if possible. Perhaps something like, "Invoices must be sent to our system."

They usually all mean the same thing. :) If referring to one road and going in the same direction, all of these can be used: "Go down that road for 2 miles." = "Go up this street 2 miles." = "Go ahead that way 2 miles." = "Go straight along this parkway 2 miles." etc. Otherwise, "Go up this road 2 miles," and "Go down this road 2 miles," can mean opposite directions.

A: The word 'game' can also mean animals that are hunted for sport or for food. A: By saying "the hunters had better be up to the job," the speaker is expressing hope that the hunters will be able to successfully hunt the animals (the game, in this case) in the forest. Saying or hoping that someone is 'up to the job' is a natural expression that is quite commonly used to express hope that someone is capable of performing a task. An example: imagine you are getting your house getting painted in a difficult way by a novice painter. It would be normal for you to say to your family member, "I hope this painter is up to the job!"

I think what you're trying to say is "예쁘다" which means "to be pretty" or "pretty."