If a word ends in -exia, such as dyslexia, anorexia and pyrexia does
this imply anything about the word itself?
It doesn't necessarily imply something about the word.
Josh61's answer (which you should read, and which I won't copy here) gives an excellent explanation of the suffix "-exia," used in the word "pyrexia" and also for some other medical conditions like "cachexia."
But, it is important to keep in mind that sometimes words end in the same sounds by coincidence, rather than because they share a suffix.
The words "dyslexia" and "anorexia" actually don't have the -exia suffix, although they end in the same letters and they do refer to disorders.
It appears that the "suffix" proper that these words have in common is simply -ia. It comes after the noun stem orex- (meaning "appetite") in anorexia, and after the noun stem "lex-" (meaning "speech, word") in dyslexia.
But, both of these noun stems are derived from verb roots using the common nominalizing suffix -s(is). So "orexis" = "oreg.sis," from the verb "orego" ("reach"), and "lexis" = "leg.sis," from the verb "lego" ("speak").
So, you could view the above two words as sharing a sort of "compound suffix" "-s.ia". But in both cases, the "e" and the first part of the "x" belong to the root rather than to the suffix.
Here's one-by-one etymological information:
"anorexia" word origin according to Oxford Learner's Dictionaries:
via late Latin from Greek, from an- ‘without’ + orexis ‘appetite’.
"anorexia" on Etymonline:
1590s, "lack of appetite," Modern Latin, from Greek anorexia, from
an-, privative prefix, "without" (see an- (1)) + orexis "appetite,
desire," from oregein "to desire, stretch out" (cognate with Latin
regere "to keep straight, guide, rule;" see regal) + abstract noun
ending -ia. In current use, often short for anorexia nervosa.
"orexis" (ὄρεξις) etymology according to Wiktionary:
From ὀρέγω (orégō, “I stretch”) + -σις (-sis).
"dyslexia" word origin according to Oxford Learner's Dictionaries:
from "dys- ‘difficult’ + Greek lexis ‘speech'
"dyslexia" on Etymonline:
c. 1887, from German dyslexie (1883), from Greek dys- "bad, abnormal,
difficult" (see dys-) + lexis "word," from legein "speak" (see lecture
(n.)) + abstract noun ending -ia. Dyslexic (n.) is first recorded
1961; dyslectic (adj.) from 1964.
Presumably the same suffix "-sis" was used here, though neither Etymonline nor Wiktionary say this explicitly.
origin of "pyrexia" according to Merriam Webster:
New Latin, from Greek pyressein to be feverish, from pyrites