While at the System Browser I can switch between panes and buttons using alt+tab and arrows, but once I'm at the "method editing" pane I can't go out of it using keyboard shortcuts. Is there a way to do so?
you can switch the focus to the other panels:
cmd+g+c focus class list
cmd+g+p focus package list
cmd+g+m focus method list
cmd+g+t focus protocol list
cmd+g+s focus source code panel
in the window menu (little arrow icon on the title pane) is a menu entry for the shortcuts description