Can I change the size of the camera view?

It is possible to change the size of the Camera View in the Output Settings.

To pan and zoom the size and position of the camera view rectangle while in camera view mode (which you can enter by pressing numpad 0), use:

shift + middle mouse --- pan by dragging the mouse around
ctrl + middle mouse --- zoom by dragging the mouse up and down
scroll wheel --- zoom in and out by scrolling the mousewheel

Make sure "lock camera to view" is off when you do that; if it's on, you'll pan and zoom the view instead of the camera view rectangle within your view. That setting is in the 3D view properties pane under "view". You can open and close that pane with the "n" key while the mouse is hovered over the 3D view.

If you need to change the aspect ratio of that rectangle (width and height), you can do that by selecting the camera and going to the "render" properties (hand held camera icon, the left most icon in the properties icon tray, at least for me) and changing the x and y values under "aspect ratio" in the "dimensions" panel of those properties.

You can use the middle mouse wheel to change the size of the camera screen in the viewport. To move the camera screen around, hold shift and the middle mouse button and drag your mouse.

If you actually want to move the camera, press shift and "f" to enable the manual motion. In this mode, you can use W, A, S, D, and, Q and E to move the camera around your scene.

You can always maximize the camera view fit the current window by pressing Home

You don't need to leave the Lock Camera to View mode for this to work.

When you are in camera view and you have Lock Camera to View enabled, you won't be able to change the size or position of the camera relative to the 3D View.

If you have this setting enabled and you want to change the size or position of the camera within your view, you just need to disable the setting, move the camera around as desired, then turn the setting back on.

The Lock Camera to View setting is in the Properties menu (N) on the right side of the 3D View.