Learn English – Word for situation in which there is no alternative

Unfortunately, no. However, the French phrase bon appetit is very widely known, and you can use that as an alternative.

A very informal option would be to say Dig in!, though this has the connotation of eating sloppily or in large amounts, and doesn't necessarily carry the idea of enjoying an elegant, modestly portioned meal.

David put his foot in his mouth.

foot in one's mouth, put one's: Say something foolish, embarrassing, or tactless. For example, Jane put her foot in her mouth when she called him by her first husband's name. (http://www.dictionary.com/browse/foot-in-one-s-mouth--put-one-s)

The mistake itself could be called a blooper. If you want something more old-fashioned: an indiscretion.

If David wants to express regret for what he said, he could say, "Me and my big mouth."