Does ATP produce E as a part of a coupling rxn?
Yes.

Does NADH2 give off 2 e-s to also produce E as a part of a coupling rxn?
Not really. The coupling of energy production to to NADH2 oxidation is very indirect,via the chemiosmotic mechanism. The term "coupling" could be used in English for this more indirect use of NADH2 oxidation for energy production. But the term coupling is usually reserved for a more direct linkage.

Does NADH2  provide E for ATP to be made? Is this there a relationship?
Yes, via oxidative phosphorylation.