You should probably ask questions in different threads when you have so many to ask. Asking 4 different questions at once means either someone has to answer all 4 or they can only give a semi-complete answer to your question which can't then really get accepted as the answer since it doesn't cover everything.
1. To get numerical positive numbers from an edit box
val = str2double( get( hEdit, 'String' ) );
if isnan( val ) || val < 0
errordlg( 'Input must be a positive number' )
end
Obviously that is a very simple option, you can expand with extra arguments to errordlg or use a warndlg instead if you prefer, etc, etc
2. To plot data on the same axes just use
hold( hAxes, 'on' )
between your calls to plot.
3. I don't really know what your question is here. Do you not know how to load inputs (if so then you need to tell us where/what the inputs are to be loaded) or do you not know how to get the options from the popup list in your switch statement?
4. There are a few ways to do this. Personally I would probably have a function that resets everything in the UI back to default state, but simpler is probably something like:
closereq;
MyGUIName;
where MyGUIName is whatever the name is of your GUI that you use to launch it in the first place. Closing and reopening a UI just to reset it is not a very elegant user solution, but it is the one you asked for.