To reply to your first problem, go to Scenes (F10) and click on the “Game framing settings” button. At the top are three buttons: letterbox, expose, and stretch. Letterbox shows the black bars along the edges. Expose shows more of the viewport. Stretch, as it says, stretches the game to fit into the window. I recommend using expose if you don’t plan on maximizing the game window.
You can also change the size of the game window using the X and Y settings (still in the Game framing settings). Also, you can click the Fullscreen button above that, so when the game opens it will be fullscreen. The image may be stretched though. Fullscreen doesn’t provide more view of the 3D area. Press esc to exit the game while it is in fullscreen. Also, Maximizing the game window doesn’t provide you with more of the 3D area either.
If you are using Letterbox and maximize the window, it will make the image bigger and maintain it’s original proportions. If you use Expose and maximize the window, it will stretch to fit the screen size; things will be distorted depending on the screen size. If you want to maximize the window or go fullscreen and maintain the original size of the game, then go with the Letterbox setting.
For your question about the camera, you can go to Edit buttons and select the camera, change the Lens value to change the size of the camera frame. Higher the value the smaller the frame. If it gets to the point where you have decreased Lens setting as far as it goes, you can always move the camera further out a bit if it doesn’t ruin the gaming experience.
I hope everything goes well with your game, happy blendering!