I remember reading about the history of this expression just a month ago or so, but for the life of me I don't seem to be able to find the link right now, so I can only answer one half of your question.
Wikipedia says that à la mode in the meaning "with ice cream" was first used in the 1890s by one Mrs. Barry Hall, from whom it got picked up by one Professor Charles Watson Townsend, who was in turn overheard by a reporter for the New York Sun, who then wrote an article about it. "Soon, pie à la mode became a standard on menus around the United States."
Etymonline chooses a more careful wording:
a la mode
1640s, from Fr. à la mode (15c.), lit. "in the fashion". In 17c., sometimes nativized as all-a-mode. Cookery sense of a dessert served with ice cream is 1903, Amer.Eng.
Finally, the PhraseFinder has this:
Americans are familiar with this phrase as meaning 'with ice cream'. There are various stories concerning how this came about but, as they aren't reliably documented, I'll not repeat them here. Suffice it to say that, however the phrase was coined in that context, it had happened by 1903 when it appears in an edition of Everybody's Magazine:
"Tea and buns, apple pie à la mode and chocolate were the most serious menus."
I take this to mean that the story from Wikipedia should be taken with a grain of salt.