Q: Associated with とはどういう意味ですか?
A: Something that is found with something (connected) or depending on context attached to something.

For example she was associated with that person - meaning she had a connection to that person.

In this example you provided theft is common with the election.
Q: He has been Associated with some dubious characters とはどういう意味ですか?
A: Dubious means "of uncertain quality, likely to be bad." Characters are people, especially fictional people. "Your character" is your reputation for being ethical and your tendency to do the right thing.
Q: Associated Presses とはどういう意味ですか?
A: A collection of news-press members following the same protocol.


Q: According to an Associated Press poll, many of U.S. young people think that high school diploma is sufficient to achieve a success. The poll included teenagers from 13 to 29 years old and 2,573 young adults. この表現は自然ですか?
A: According to an Associated Press poll, many young people in the U.S. think that a high school diploma is sufficient enough to be successful. The poll included 2,573 responses from those between the ages of 13 to 29 years old.
Q: Associated , did I say it in a good accent? この表現は自然ですか?
A: Sounds great, although the 't' is pronounced more like a 'd'. It's actually a 'flapped R' like in Japanese.