Initial knee jerk thoughts :D

1- when i clic on a label the procedure clic is called but focus (or selection) gave back the label that have focus before clic but not the clicked one (that is to say it gaves the previously clicked on) so it is necessary to clic again to get the good value

Yeah, "focus" is the dark blue color, and I see it changes like its supposed to on first click

Anyway, <1> is not the event you want, there are other ways to select a node, see the docs http://tcl.tk/man/tcl/TkCmd/ttk_treeview.htm

Similarly "->focus()" isn't what you want

2- when i clic on a node + to open it, the procedure clic is called i expected it was called only when clicking on the label, not on the + sign

When I click on + a newline gets printed on my shell, which means clic must have been called, because its doing the printing

3- the two defined scrollbars are visible vertical one works fine when necessary but horizontal one never become active, even when necessary (resize the window to see)

And what tells the scrollbar it should change? Something in Tcl land somwhere ... good luck with that :D

4- there is a blank line at top of the tree display here is the script

blank line? I see a "column" "heading" button, not a line, its grey, its documented