No it is not true that Mazurkas are all fast. My edition of Chopins 50odd have quite variety of tempi markings, including several maked Lento, the best known of which is an early A Minor one. Theres another A minor marked Lento as well, though it seems to require a bit quicker tempo than the first one. They are almost all in 3 time, but some have introductions in other time signatures. A Mazurka is of course a dance.
Nocturne simply means 'Night Piece'. The inventor is supposed to have been the Irish compser John Field (contemporary with Beethoven). Chopin took up the format , and many others since eg Poulenc, Britten. They too can vary in tempi quite a bit, but often (though not always) start with a relavtively calm part, and a stronger section in the middle.
Preludes of course come in all shapes an sizes, from Bachs '48' through composers like Chopin, Rachmaninov, Scriabin, Shostakovich etc (to name but a few) to the present day.
I guess from looking at just a written score, the Mazurka would be the easiest to spot. If its clearly not one of those, then try to see if the name 'Nocturne' might apply. If not, its probably a prelude. !
PS Welcome to the forums Pseudonym !