Preventing Winform from being maximized?

There are actually two completely separate issues at work here. Granted, they look basically the same from a functional perspective, but from an implementation-model perspective (as Windows itself would naturally use) they are unrelated.

As others have answered, you can prevent your form from being maximized by setting its MaximizeBox property to false. This removes the WS_MAXIMIZEBOX style on the form's underlying window, which prevents the window manager from allowing the window to be maximized. It disables the maximize box on the window's caption bar (the one between the minimize box and the close box), disables the "Maximize" option on the window/system menu, and any other methods of maximizing a window that I may have forgotten.

However, this has nothing to do with the Win+↑ keyboard shortcut, which invokes Aero Snap the same as would dragging the window to the the magic position sat the edges of the screen. The window manager, whether as a result of a bug or a feature of Aero Snap, still allows you to effectively "maximize" windows that should not otherwise be maximized. Setting the MaximizeBox property doesn't affect this, so if you truly want to prevent the user from changing the window's size this way, you will need to disable Aero Snap's effect on your window.

Unfortunately, there's no method (at least, not to my knowledge) of programmatically disabling Aero Snap on a per-window or per-process basis (also see this related question). If the user has Aero Snap enabled, you can assume that they want that behavior and applications aren't supposed to tamper with it. The only thing you can do is completely disable resizing your window. In WinForms, you do that by setting the FormBorderStyle property to one of the following: FormBorderStyle.FixedSingle, FormBorderStyle.Fixed3D, or FormBorderStyle.FixedDialog. If you still want your window to be resizable in other ways, you will need to write the code to handle that manually, which is not a particularly easy task.

Thus, I encourage you to very carefully consider whether this is really necessary. All other non-maximizable windows accomplish this simply by setting the MaximizeBox property (or doing the equivalent in their UI framework), which means that they can still be effectively maximized via Aero Snap. If this works for everyone else's windows, including those that are part of Windows itself, it should probably work for you.

The form has a property called MaximizeBox - set this to false.

In regard to your second question, check out this question and it's answers for the best ways to implement keyboard shortcuts in WinForms.

this.FormBorderStyle = FormBorderStyle.FixedSingle;

That line of code will prevent the user from re-sizing the Window.

In addition to that you hide/disable the maximize box and that should do what you asked.

To disable the maximize box use this

this.MaximizeBox = false;

To hide the maximize box use this as well

this.MinimizeBox = false;

If Maximize and Minimize are set to false the buttons disappear.