Does FIDE give titles to chess composers?
If so, do share more insight about the how-tos and other links to read.
They used to, but now the titling process is handled by the World Federation for Chess Composition.
Here's a link to some of the titles:
The answer used to be Yes, via the Permanent Commission for Chess Compositions; in 2010 the Commission became the independent World Federation for Chess Composition, but "both organisations are cooperating". As was the case before 2010, there are three titles: Master, International Master, and Grandmaster, all based on the counts of problems and studies published in the FIDE Albums.
There are also titles and ratings for chess problem solving, and a title of International Judge of Chess Compositions.