1) Are you referring to Dedekind cuts? They have nothing to do with decimals. You can't count all the decimals (see 2).

Every rational number can be expressed as a decimal.

I gave a very explicit proof, using accepted principles, that the decimals can be counted. See OP.

https://en.wikipedia.org/wiki/Cantor's_diagonal_argument
The wiki article gives Cantor's "proof" that a binary sequence is uncountable, which I find obtuse and contorted.

Then the wiki author "proves" that every real number can be expressed as a binary sequence, but doesn't define real number.

A binary sequence, by definition, is a rational number. It then follows from Cantor's proof that:

a) The rational numbers are uncountable.

b) Every real is a rational number

With that, I have exposed the flaw in my own argument:

By definition, a decimal is a rational number. So an irrational number can't be expressed as a decimal, just approximated by it.

And now we have another proof that Cantor's proof that a binary sequence is uncountable is wrong:

Every binary sequence is a rational number and every rational number is a binary sequence. If Cantor's proof is correct, the rational numbers can't be counted. And then his argument that reals can't be counted fails.