Considering you are in Principles of Chemistry (an introductory course), the following is an over simplification, but should help you understand the main idea of spectral emissions.
(1) Hydrogen (H) has 1 electron, and this electron is in the 1s orbital. It can be promoted to 2nd, 3rd and even fourth energy levels, e.g. and each one of these will produce another line in the spectrum when it falls back to 1s. So, you can get more than 1 line .
Looking at helium, you have 2 valence electrons (both in 1s) and again each of these can be promoted to higher energy levels. If each were to get excited (promoted) to the 2nd and 3rd energy levels.
Sodium has only 1 valence electron in the 3s orbital. It can move up to the 3p and fall back. Since there are more than 2 "states" for the p orbital, you can get 2 lines instead of just 1.
Neon has 8 valence electrons, and by the same reasoning as suggested for hydrogen and helium above, you can see 16 lines.
(2) Yes, they could be producing other types of EM radiation. If the electron(s) in the atom gets excited to a higher energy level, say n=5, n=6 or n=7 e.g., the energy liberated when it falls back to the ground state will be of greater magnitude, and not seen in the visible spectrum.