These are terms of art in linguistics. NPe are ellipses in noun phrases, i.e., with certain language constructs omitted. Let's take the easy one first:
e contains methanol
This is from a label on a pill bottle. Only the words "contains methanol" actually appear on the label, but to understand the sentence, we must assume there is a missing subject, denoted by e, "the pills in this bottle."
Next we have pro (called "little pro" in the biz), and it refers to omitted pronouns that could well appear in the sentence. Check out the discussion in Linguistics: An Introduction by Andrew Radford. He gives the example of Trinculo's line from The Temptest (Act II, scene ii), which I've annotated as
Hast e any more of this?
Hast pro=[thou] any more of this?
The actor playing Trinculo doesn't say "thou," but that's what his line means, and the sentence would be grammatical if he included it.
PRO (called "big pro," naturally) is an unsaid and never-said pronoun assumed in some theories to exist in certain phrases under the assumption that all such phrases must have subjects even if they're implied. In the example
Mary tried e to fly
it is assumed that the infinitive has an implied subject that is Mary herself. This may be written as
Maryi tried PROi to fly.
That is, it's the subject Mary who tried to fly. But it's possible that the PRO may be indexed to the object:
Mary asked Johnj PROj to pay.
In the flying example, the subject controls the PRO; in the asking example, the object controls. Thus the term "control PRO."