Total Commander

I'd like to see ability to define own context menu for bar icons.

Let's say, I got "Syncthing" shortcut on my bar (the software for syncing data between devices). I want to add two positions to submenu (which by default contains shortcut name, "as Administrator" option, Edit, delete, go to dir etc): go to defined directory, where I store my data, setup software (run syncthing.exe with parameter), maybe something more.
It also could be really useful if I could use parameters like %programpath% or system variables to define submenu shortcuts.

Perhaps the openbar command already does what you want, create a button bar for your Syncthing, then in your "mainbar" create a button with the command:

openbar path-to\Syncthing.bar

now a drop down "menu" (the bar) will appear.

In addition to hi5's recommandation you have to check the option: "Show as menu" in the "Change button bar" dialog.

You don't need the openbar command, just writing path-to\Syncthing.bar in the Command field for the button should do it.