I don ´t know IE7 and I really don ´t want to get to know it, but if you can do those things with keyboard hotkeys, you can map them to gestures.
I give you an firefox example shortcut, you have to find out the IE-shortcuts by yourself ;)
the firefox hotkey for new tab is CTRL+T
-open StrokeIt
-create a new Application (CTRL+A)
-name it IE7 or whatever you want
-click add, open your IE7 and drag the finder-tool over your IE
-create new Task/Command (haven´t english version) (CTRL+T)
-name it new tab or whatever you want
-map with a gesture of your choice
-create execution-command (CTRL+N)
-choose "Keyboard: HOTKEY"
-focus the Hotkey-Label and Press CTRL+T
-configure all the hotkeys you want to map the same procedure
StrokeIt is somewhat easy, I really love it!