"He has many samples now."
Translation:Tá a lán samplaí aige anois.
One thing I remember hearing from my teacher in the Gaeltacht is that go leor is used in positive sentences, which mórán is generally used more in negative/question sentences. How true this actually is, or how widely held I can't claim.
Why is it "a lán samplaí" and not "samplaí a lán"? Is there actually a genitive phrase involved here?
There is actually a genitive phrase here. a lán samplaí is essentially "its full(ness) of samples".
You can see that it's a genitive construction in cases like chaill sé a lán fola - "he lost a lot of blood", but in the case of samplaí, the genitive plural is the same as the nominative plural.