I am a bit tired of "Gaussian". i do not use it since years ago and perhaps my memory fails but now i can say

R1) I suspect your mean why offers negative energies for molecules and so. This is because, it is needed a "system of reference" and by commodity, Gaussian takes that of particles without interaction. Then E(p + e) = 0 but E(H) < 0

why negative? because system is stable. In fact, positive energies denote unstable states for the composite system when compared to its free parts.

R2) In manuals of computational chemistry, in journals of computational chemistry, etc. In molecular structure, people reports computations for molecular species and data obtained: bonds, energies, constant forces, etc. Try to ask to some computational chemists who can direct you to specific source without many search. Have you try in CAS or NIST?

R3) Errors asociated to input: e.g. what is the value of Planck constant taken by Gaussian?

Errors asociated to use of Schrödinger equation. Equation does not work in more general cases. Schrödinger equation is just valid for CLOSED systems in pure quantum states suffering reversible processes. Chemists working in advanced electron dynamics or NMR usually work with Redfield equation. Physicists working with fullerenes in external fields work with Caldeira & Legget equation. I am searching more information (including a graphic of error of the use of Schrödinger in fullerenes at different temperatures i saw some time ago) about all this and return for posting (a week or so)