a dangling modifier is a phrase that does'nt modify the noun that's near it?

Answer 1

Yes.

Did you want an example? This wasn't clear from your question.

"The airplane radioed the tower flying around the airport." In this sentence, it sounds like the tower is doing the flying. A correct sentence would be,
"The airplane, flying around the airport, radioed the tower."

Answer 2

you're right, and wide awake is correct! :)

other examples would be as follows:

i saw my neighbor carrying a brown, stray cat with a yellow hat. (dangling modifier)

corrected: i saw my neighbor with a yellow hat carrying a brown, stray cat.

the girl went to the washroom with a pink dress. (dangling modifier)

corrected: the girl with a pink dress went to the washroom.

that boy is going to the library riding a bicycle. (dangling modifier)

corrected: that boy, riding a bicycle, is going to the library.

hope you understand by now... :D