A few separate questions here so to take them in order:

1) Cracked screen: Have you looked into replacing this ? Would be the
better solution all round and the screens themselves aren't expensive.
How to do the job - http://www.youtube.com/watch?v=RPUDwOd5DPs

2) Getting OS to use external by default: You should be able to start
the installation from external USB ( either flash drive or CD drive )
by having it plugged in then tapping the [F12] key during boot. The
initial screens should appear on both internal and external screens
but once the WinXP installer gets to the configuring hardware bit you
may need to use the manual switch on the Dell to see what's going on.
One of the function keys should do this, usually holding down the
[Fn] key whilst pressing [F6] or [F7].

Alternatively you could use Virtual Box and install WinXP in that so
you'll not lose your Mint installation :-)

3) Running .exe files: Yes you can run these using Wine, or Play on
Linux, but the results will vary according to what you are trying to
run. Some programs will work, some will work but not 100%, some will
refuse to work no matter what you do. Question is, what program(s) are
you wanting to run ?

4) VMWare is a bit heavy IMHO and Virtual Box is lighter. How well it
works you can only determine by giving it a try and you've nothing to
lose apart from a bit of time so why not load up Virtual Box and see
how your WinXP runs in that ? You don't need to give it a load of
memory during the setup, 128Mb or 256Mb will be fine - the bulk of the
memory load is still with the host OS when running virtual OS's :-)

Hope this is useful but I'd still recommend you look into replacing
that screen - not as daunting as it may seem, just need to know which
end of a screwdriver is which and take it carefully