0 is generally not recognized by Lacerte as ZERO. If ZERO is wanted you would enter -1. In this case, I think leaving the entry blank works.

When you add the depreciation, use 7/1 as date put in service for the cost of the home & improvements up to date, but I would add land with an original purchase date, just for reference purposes. Allocate land/improvements based on some logic for when the home was originally purchased. Property tax bill at that time is a logical method, but not necessarily correct or the best method. Honestly I have never had an audit on that issue in 50 years.