The only dwarves that are given specific ages by Tolkien are Thorin (195), Balin (178), Dwalin (169), Oin (167), Gloin (158), Fili (82), and Kili (77).
In The Hobbit, Tolkien states that Fili and Kili are the youngest "by some fifty years." So the next youngest dwarf is (at the very least) 132-year-old.
Now, here's an excerpt from The History of Middle-earth: Peoples of Middle-earth:
Balin is obviously an exception to this, as he's described as "very old-looking," even at the age of 178.
As far as the beards are concerned, all dwarves are born with beards (including the women). They will trim them to keep them looking neat and clean, but they won't cut their beards off unless they've been shamed, or if they absolutely have to (like Fili in the book). If it turns out that Kili is too young to grow one in the film (hence the five o'clock shadow), then that is a departure from the source material. There's no disputing that.
The best explanation for Thorin, Kili, and Fili having short beards is that they shaved them out of shame, which is true to Tolkien's text.