With vs without egg fresh pasta cooking time
Egg v. no egg does not influence cooking time for fresh pasta. There are plenty of egg free versions.  This is a go-to for me, and produces a great pasta.
Thickness...whether or not it is filled...cooking from frozen all influence cooking time a bit.  In an interview with a well-known pasta chef, I heard him state that most people (in US) over cook dried pasta and under cook fresh pasta.