I am not familiar with Total Commander, but some of the wishes you have are already in BetterZip, although they probably work a little different from it.

To adjust the font size press Cmd+ and Cmd- which many Mac OS X programs use.

Home is Option+Up, end Option+Down. To collapse/expand a folder use left and right arrows. To expand all subfolders use Option+Right. But, sorry, the folder has to be selected for that.

The synchronization feature is on my to-do list in form of updating archives automatically, but it will have to wait a little.