Your statements about the world provide a theory that can be used to do an experiment to support or disprove your theory, but there is nothing that can prove that theory like proofs in a mathematical theorem.

Scientific theories are used to support a wide range of phenomenon, but are later superceded by better theorems that can encompass more phenomena. Experimental evidence can provide support for the theory, can disprove a theory, but cannot prove the theory.

Unrelated to mathematical proofs, but there are counter examples for each of your statements.

1.

The acceleration due to gravity on earth is not constant, it varies depending on location (easy to experimentally refute that it's not 9.8 everywhere). For example, being on mount everest versus at sea level in the Arctic would give different rates of acceleration.

Adding a tilde in front of 9.8 m/s^2 doesn't help make the statement look like a proof.

2.

Given that acceleration due to gravity is not constant, then the trajectory will no longer be a parabolic curve.

This is bad-faith misreading. I never claimed that acceleration due to gravity is exactly the same at all points on earth. There are very small local variances, all accountable by known principles of classical mechanics. I never said or implied that adding a tilde in front of 9.8 m/s^2 helps make the statement look like a proof.

I'm not interested in nitpicky arguments. Good bye.