Let me get this straight! Anytime the U.S. has an Election

[FBaggins]

1. Not quite

The argument is that international agreements that have the force of law within the US are called treaties and need to ratified by the Senate. Other agreements (absent an implementing law) are little more than agreements between that President and the other parties.

One President doesn't have the ability to bind the next one (again... absent laws or treaties).

That doesn't mean that all prior agreements are "null and void"... just that the next President can ignore them by changing the administration's policy.

If I were any other world power, friend or foe of the United States, I would therefore refuse all long-term negotiations with the U.S. as they would no longer be honored through the next election cycle.

No... you would just insist that those deals be formal treaties that get ratified.

Will this hold true for a certain trade deal that is being negotiated as well?

NAFTA (as an example) is a treaty and was ratified by the Senate. The President cannot ignore it.

How about this on a domestic scale? Any laws that actually managed to get passed between a sitting President and a sitting congress are only guaranteed valid, until the next election cycle as well.

Nope. He can't ignore existing law (not that President's don't on occasion try).