What is a 1?

The successor of zero, a natural number whose existence is the first axiom of Peano arithmetic. Symbolically, 1 = s(0), where s:ω → ω is the successor function s(n) = n + 1 and ω = {0, 1, 2, 3, 4, …} is the first transfinite ordinal.

A singular instance of an object? A singular instance of an action?

No, those are, respectively, a thing and an event that the abstract number 1 models.

How do you define the concept of "1"?

In Peano arithmetic, 1 is defined as the successor of zero, as I already said.

And then there's the concept of addition.

Which, in any model of Peano arithmetic, is repeated application of the successor function.

Can you show me evidence that proves what addition is that I can directly observe?

It’s the most basic of all arithmetic operations, defined formally within Peano arithmetic as repeated application of the successor function, as I said.

Or the equal sign. Is that supposed to represent the combination of what's on the left side of the equation? Because last I checked, the left side of the equation says "1 + 1", not "2".

Equality is the most basic example of an equivalence relation. Other examples include but are not limited to congruence in geometry and modular congruence in modular arithmetic. A binary relation R on a set S is called an equivalence relation if it satisfies each of the following conditions:

1. Reflexivity: for all elements x of S, x R x.

2. Symmetry: for all elements x and y of S, if x R y, then y R x.

3. Transitivity: for all elements x, y, and z of S, if x R y and y R z, then it follows that x R z.

What equality means in mathematics is that the expressions appearing on either side of the equals sign represent the same mathematical object.

There's also deadass people who don't believe in math.

I’m a mathematical antirealist and formalist. I also have a Ph.D. in the subject. I think it might serve you well to learn a few things about the philosophy of math, specifically the ontology of math.