Masks can be tricky and, as with layers, it is sometimes possible to run into seemingly incomprehensible difficulties. The reason is almost always because the active layer is not what you think it is. The following lists some common problems you might run into with masks.
The problem is that the selection is still active. This means that modifications to the mask are allowed only in the selected region. Cancel the selection using Image:Select/None or by typing C-S-a in the image window.
Saving a selection to a channel automatically makes the new channel mask the active layer; however, if you check the Channels dialog, you'll see that the active channel is not visible. Thus, the paint and filtering operations you are trying to use have been applied to the channel mask, which can't be seen. Either toggle on the channel mask visibility by clicking on its Eye icon in the Channels dialog, or make the desired image layer active in the Layers dialog.
Cutting a selection in a mask has the effect of making the selected mask pixels the background color (as shown by the Active Background Color patch in the Toolbox). If the selection is made in a black part of the mask, make the background color white. If it is made in a white part of the mask, change the background to black. Typing d in the image window sets the default colors, which are black for the Active Foreground Color and white for the Active Background Color. Typing x switches the foreground and background colors.
The layer mask is not active. Make sure you select it by clicking on its thumbnail in the Layers dialog.
No, the GIMP is not broken. Check the Mode menu in the Brush Selection dialog. If the blend mode is not set to Normal, this explains your problem.