We have to confine our answer to the major league level. Yes, in the majors, there have been left-handers who played second base, shortstop and third base. Wee Willie Keelar, a Hall of Famer, played second base, third and shortstop 71 times over his 19-year career from 1892 through 1910. Hal Chase, normally a first baseman, played 36 games at second base between 1905 and 1916. Bill Hulen of the 1896 Phillies played 73 games at shortstop and two at second base in his only season with the club. First baseman Don Mattingly of the Yankees played one game at second base in 1983 and three games at third base in J, 986 despite being left-handed.
Wade Boggs batted lefty but threw righty
Rogers Hornsby is the most common answer to that question. Rogers hit .358 (second highest career average), with a career OPS over a thousand. He is often considered the greatest right handed hitter in baseball history.
Robbie Alomar (probably the best second baseman ever)
No. He has always been right handed.
There have been a few left-handed throwing catchers; the most prolific of them would be Jack Clements, with over 1,000 games caught.
Yes, dog killer!
Yes, sort of. I don't know of any who both bat and throw left, but there are a few who bat left and throw right. Current examples of left-hand hitting third basemen include Hank Blalock http://www.findarticles.com/p/articles/mi_m0FCI/is_7_63/ai_n6108322 and Russ Branyan http://www.baseball-reference.com/b/branyru01.shtml Don Mattingly played one game in 1986, Mike Squires played one game in 1983
The best ever left handed batsman in England is Sturss (Captain)