1. in thunar the first column is called "Name", in squeeze it's called "Filename".
i think "Name" is better, since folders are in that column too.

now to the real issue:
how about dropping the toolbar or make it disableable (what a word ;)), because i don't think the options are used that much:
- squeeze needs thunar-vfs and aims for xfce integration. i use the t-a-p to extract and create archives fast.
- is "new" such an often used action? i think a "File > New" menuitem is enough. - same for open. how often do you open archives from within squeeze? sure, this enables tabs, but how about sth like a browser and open an archive in a tab, when squeeze is already running? this way only one program window would be open. of course this should be configurable too.
- "add" and "extract": they could easily be moved into a context menu in the archive treeview. at least extract. adding files isn't a very common action, only for new archives. i personally use the t-a-p for that, as it's faster. and you still have the menu item.
- "delete" is also not often used. and it could be put into a treeview context menu too.
- "stop" should be a button in a separate window with a progress bar, when files are added or extracted. having stop in the toolbar would only be usefull when opening a very large archive and you want to cancel that. perhaps a progress window would be better. maybe show one, when the archive is >100M or so, dunno.

when the toolbar would be removed, you would only have one line of buttons, when you enable the tool bar or path bar navigation style. then squeeze would look exactly like thunar, which would improve the xfce integration gui wise. and as described above, the toolbar items aren't very often used.
i think there is even a point in the HIG somewhere which says 2 toolbar lines are bad.

i hope this doesn't seem like one of those huge combo bug reports, but i tried to explain why i think the toolbar should be off by default.
(another cool thing would be using libsqueeze directly in thunar to open archives in the fm, but that's really another thing ;))