How can any of these be the answer when all the choices use nice -n and the man page says for -n?

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man nice says

1) So I tested this by running nice -n 3 top. top got a nice value of 3, but shouldn't it be 13 since it's adding? default is 10 + 3 (I added).

2) Also if the default is 10, then why does top get a nice value of 0, when I run it without the nice command?

The man page also says
3) So I run nice with no arguments, and I get 0. Shouldn't it be 10 sense the man page says the default nice value is 10?

4) When running nice with no arguments by itself, does the number given mean that is the nice value of the current shell it's being ran in (such as bash), the nice value that will be given to processes launched from that shell, or something different?

The default value of the adjustment is 10, i.e., the amount that is added to the niceness of the current process. When you run "nice -n 3 top", the adjustment of 3 is added to the niceness inherited from your shell, probably running with a niceness of 0, and the result is 3. When you run a process via nice and do not specify an adjustment, you get an adjustment of 10. Running nice with no arguments at all is a special case where the current value is reported and there is no adjustment at all.

Scheduling priority is not the same thing as niceness. The scheduling priority is the sum of the niceness and a base priority calculated from CPU usage and other factors.

The scheduler considers many factors, of which "niceness" is only one. This parameter in-effect allows you to contribute your personal opinion about what the scheduler ought to do with this process. It's a very important input since it represents something that the computer would have no way to determine on its own, as well as something that is from your point-of-view.

See also "renice"

Merged your dupe/closely related threads. Please refrain from multi-posting.