1. The MLB season proper has not. The postseason, specifically the World Series, has played into November twice, and could have a third time had it gone to Game 7 (which that year it did not).
2. Charlie Root, as legend has it. 1932 WS, think it was Game 4.
3. LCS began 1969, Division Series began 1995 (would have begun 1994 but that season ended in August, and there was the one-time Division Series in 1981).
4. Hubert H. Humphrey, former Vice-President and Senator from Minnesota. (I think the middle H was for Horatio, but I'm not looking it up.)
5. Majors? Most of them. Minors? I think there's some pro baseball in every one except Hawaii. Collegiate? High school? The nation is carpeted with these.
OK, majors -- 33 have no MLB team: Maine, New Hampshire, Vermont, Rhode Island, Connecticut, New Jersey, Delaware, Virginia, West Virginia, North Carolina, South Carolina, Kentucky, Tennessee, Indiana, Alabama, Mississippi, Louisiana, Arkansas, Iowa, Nebraska, Kansas, Oklahoma, North Dakota, South Dakota, Montana, Wyoming, Idaho, Oregon, Nevada, Utah, New Mexico, Alaska, Hawaii, matrimony, and intoxication.
The other 17 states have at least one MLB team, plus there's one in Washington, DC, and another in Ontario, Canada.
----------
Edit: there have been THREE other times the WS could have (but did not) stretched into November, but two of those were due to delays and not on the original game date schedule. Those were 1989 (earthquake) and 2008 (torrential rain). The 2007 original schedule had Game 7 on 01-November. The Series actually has reached November in 2001 and 2009, and probably will again.
----------
Ed2: Ha! His middle name IS "Horatio".