Answer to Question 1
Asteroids whose orbit crosses ours, with perihelions of less than 1 A.U., but semimajor axes still more than 1 A.U. These are potentially the most dangerous of the Earth-Crossing bodies.
Answer to Question 2
They are too cool to ignite nuclear fusion, so shine feebly only by the energy of gravitational contraction, and that does not last nearly as long as main sequence fusion would. We now have infrared surveys, such as 2MASS, that can pick up the heat of these cool stars much better than in visible light.