The report parameters are indeed Visible=false and this is by design. They are setup this way so that the built-in parameters area is not shown if not needed (it is not customizable and provides basic out of the box handling only) and you can still pass values to the params from your actual app i.e. introduce your own UI.
As for your second report - we were not able to reproduce such an issue. The Visible property of the parameters is serialized properly and had not changed after playing with the groups. If you can replicate this steadily, please provide us with steps to do so.
the Telerik team