The Error initializing Steam API error occurs when the Steam API could not be initialized. This may happen sometimes, unfortunately it's a Steam thing, so it's out of our control. To fix it, simply restart your Steam client, usually this does the trick 
About the fps issue: One reason for the limited framerate may be a low refreshrate in combination with vsync. Make sure vsync is disabled in the graphics options. Maybe you can also post a report file, this would give more information about the current fullscreen mode. To do that, open the console ingame (by pressing ` or ~ or ^) and type "report" (without quot. marks), then a file called "report" will appear in your game directory. Please post this file here 
Alternatively you could use the undecorated mode, as suggested by @SimonK. To do that, adapt the resolution to your desktop resolution, disable the fullscreen mode and check the "undecorated" box. This provides an alternative fullscreen mode which runs more smoothly in most cases^^