In order of frequency:

#1) Where can I obtain a full-length copy of Lou Gehrig's famous farewell speech

The short of it is you can't.  None exists.  Ever notice that sources differ on the exact wording of his speech?  There's a reason for that.  As unfathomable as it is to us today, no one back on July 4, 1939, had the presence of mind to record all of Gehrig's famous "Luckiest Man" speech.  Over 60,000 people in Yankee Stadium that day, and not one of them thought to record the entire speech.  There is a ray of light, however, for those Gehrig fans that want to hear as much of his speech as possible.  The YES Network, the Yankees' own cable TV station, has a series named Yankeeography which highlights a different Yankee each episode.  Lou Gehrig's Yankeeography includes rare footage of July 4, 1939, and also includes all the known clips of his speech.  Want to buy a copy of this show?  Find it in Shop MoreGehrig.

#2 What happened to Gehrig's family after he died?

Answer: After Lou's death, his parents moved to Mt. Vernon, NY. They sued his widow, Eleanor, for part of Lou's insurance money, but it was settled after two years. His father passed away in 1944, and his mother in 1954. Both are buried next to their son (and Eleanor) in Valhalla, NY. Eleanor was an ALS advocate and worked for a while for the All-American Football Conference. She consulted on the movie "Pride of the Yankees." She passed away in 1984 from apparently natural causes. You can read more about the remainder of Lou's parents' lives as well as Eleanor's in my book, "The Life of Lou Gehrig, Told by a Fan," available in Shop MoreGehrig.

#3) Did Gehrig have children?

Answer: No, unfortunately. He and his wife were unable to have children. No one is quite sure why, though some speculate that Eleanor's medical history (heart concerns) was the main reason. Both Lou and Eleanor wanted children and discussed adoption. But Lou's mother, for whatever reason, refused to give her blessing for adoption. Since Lou often did what his mother wanted him to, he gave in, and he and Eleanor went childless.

#4) Where is Gehrig buried?

Answer: After his death, Lou was cremated and the remains were buried in Kensico Cemetery in Vahalla, New York.

#5) What was Gehrig's favorite food?

Answer: The legend is he loved pickled eels, a German delicacy that his mother made constantly when he was a boy. The eels are supposedly what gave him his power hitting. Whether Gehrig would actually identify his favorite food as pickled eels is doubtful. Though he did share a batch of eels with his teammates on his mother's insistance, Eleanor claimed that Lou favored fruit and fruit juices.

#5) Do you know what happened to any particular item in Gehrig's estate?

Unfortunately, it's difficult to track down one particular, non-baseball-related item.  When Gehrig died, most of his belongings went to his wife; some things went to his parents.  When his wife died, most of his baseball-related belongings were donated to the Hall of Fame.  Past that, I haven't found much as to the fate of every item in his estate (although I'm still searching).  If you're wondering about one of his baseball-related belongings (mitt, uniform), I can probably tell you the item's fate.