You have it basically right. Any money you draw out of the business for personal use during the year is <Owner Draw>. Because of the nomenclature of LLC and that you are considered a "member" I always call it <Member Draw> but that is semantics as long as you know what you are dealing with.

I do directly "reduce" or reimburse the draw when I put money back in but to be accountingly correct  you should have a corresponding <Owner or Member Contribution> equity account where all money in goes. 

Yes, Member Draw is a negative number since it represents money taken out of the business.

Once a year, upon closing the books, <Member Draw> should, along with the fiscal Profit or Loss, get posted to the overall <Owner/Member Equity> account, leaving the Draw account fresh at zero for the next year. At year end you are passing through the P or L to your 1040.