If numbers are infinite then does that mean there is an equation for everything?

The issue is you're defining infinitely in a bad sense, you have to know what you're talking about such as countable, uncountable, etc.

Technically if what you mean by equations is just an equals sign, take:

{x = y | x is in R} c {all equations}

then we see that since R is uncountable, this subset of all equations is uncountable, hence the set of all equations is uncountable.

(Now, what level of uncountable it is, I don't know. I don't know that much about foundations to talk about aleph and what not).

For every real number, there is an equation that has that number if that is what you mean. Your question is vague.

The infinity of numbers really has nothing to do with equations, so no.

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