Rather than finding the "gta2 manager.exe" in the Finder and opening it from there, it's better to use the Run Command dialog (from CrossOver's Programs menu). Opening from the Finder will only work if GTA2 is in your default bottle. With the Run Command dialog, you get to pick the bottle you run the program in.
Command-Tab and Spaces don't work because the game is in full-screen mode, and CrossOver "captures" the display for full-screen mode. This is necessary so that other Mac apps don't rearrange all of their windows, etc. if the game changes the display resolution. Mac OS X prevents the use of Command-Tab, Exposé, and Spaces when the display is captured.
You can try playing the game in a window. If the game refuses to run in a window, you can force it to by having CrossOver emulate a virtual desktop in a window. To do that, launch "winecfg" from the Control Panel tab of the Manage Bottles window. In winecfg, select the Graphics tab and enable emulation of a virtual desktop.