I have a question:
If Non-Spellcasting Area is on the field, and I use Fake Hero to special summon Elemental Hero Neos from my hand, would he return to my hand at the end of the turn?

No...it does not...obviously. Returning to your hand is part of the EFFECT of Fake Hero...

Non-Spellcasting Area
Continuous Magic
All face-up Monster Cards on the field, except for Effect Monsters, are unaffected by any Spell Card (excluding this card).

Thank you very much, I just wanted to make sure before I did anything potentially stupid.

It's also easy to remember...just compare it to E. Hero Wildman/Tenkabito Shien and Return from the Different Dimension (they are unaffected and are not re-removed).