I am curious to know if the Executive Orders of a U.S. President would be nullified if he/she is removed from the Office of the Presidency via the 25th Amendment, especially if it is proven that he/she was mentally or physically incapacitated on the day(s) when those Executive Orders were signed.
No. They could be, but the "nullification" wouldn't be automatic. That is because, as the Congressional Research Service says in its excellent "Executive Orders: An Introduction":
"Once issued, a valid executive order has the force and effect of law. Executive orders do not, by default, expire when the issuing President leaves office. Instead, an issued executive order remains in effect until it is either struck down in court, modified, or revoked."
Because executive orders persist but can be easily changed, one of the first orders of business of a new administration is to revoke, modify or re-issue inherited executive orders.
As far as your hypothetical, most commenters agree that when the President is expected to return to office quickly, the Acting President's job is simply to "keep shop." However, in extreme cases, such as the one you outline, they also agree the Acting President can exercise the full-range of Presidential powers. Thus, the Acting President could revoke the problematic orders. (This is discussed in Yale Law School's in the Yale Law School's "Reader's Guide" to the 25th Amendment.)
If you want to know more, the Wikipedia page on Executive Orders gives a short (and harmless) summary. For more detail, see either the CRS pamphlet cited above, or their earlier pamphlet,"Executive Orders: Issuance, Modification, and Revocation."