The modifier key indicator is attached to the memory indicator. If you dont want to see it, turn off the memory indicator
There is no toggle for the key indicator; it's there to debug "stuck keys" (though none have been reported for months, so I may remove it next update)
Ctrl+\ is to toggle
auto-tiling. Auto-tiling has to be enabled in both the main program and in each session (or profiles), and the hotkey actually only toggles it in the main program -- so that any sessions loaded in the future are not going to be tiled automatically when it is off, but all sessions with auto-tiling on will tile when it is on. To switch from full screens to tiled and back, you would actually need another hotkey. The best thing to do might be to use Picture-in-Picture, if you only need to keep an eye on two? Give it a try anyway and maybe you'll be happy with it.
Past that, you could try Inner Space. IS is the "rewrite" of WinEQ 2 (WinEQ 2 has a bunch of fundamental issues that needed solving, though it is easier to use because of the preferences window) and mixed with some other concepts. IS has almost all of the default WinEQ hotkeys and such, but does not natively have a "tiling" system. Rather, it has a system that would allow you to tell whatever window you want to go wherever you want and look however you want. It is more difficult to set up (since nobody has done a tiling script to date, not because it takes a rocket scientist to load EQ), but will get you exactly what you're looking for if you have the ability to make it via supplied commands. There is an example of a Picture-in-Picture system for any number of windows though, and each will go across the top of your screen
