Do cash distributions have to be equivalent (per partner percentage) for each LLC partner during the year? If they do and they weren't, should I book a payable for the company?

As a matter of Generally Accepted Accounting Principles, the distributions should be equivalent to partner percentage.

If the distributions were NOT made, I do not think you woul book it as a payable to the company.

However, certain punitive taxes will be assessed if the reasons for failing to make the distributions are not in keeping with IRS regulations.