N and M are the nasal consonants, that is our breath goes through the nose instead of out the mouth when we say them.

An anusvara is a diacritic used in the Devanagari script to indicate a nasal consonant.

No, "solemn" does not contain a sounded consonant. The "n" at the end of the word is a nasal consonant which is typically not pronounced in English.

It is called a consonant blend or a digraph

A consonant blend is when two or more consonants appear together and you hear each sound that each consonant would normally make. -- As in fingerprint

A digraph is when the two letters represent a single sound. -- As in fang

If described according to it's point of articulation it is a velar nasal consonant

level, lever, revel, basal, canal, devil, fiver, galas, humor, joker, kilos, lulus, mamas, nasal, papas, radar, sagas, total, vivid, Zimas