Currently the single view has the same itemid as the map page - this means that the modules that you publish on the map page will be displayed in single view as well.
It is possible to have different sizes for the maps. You must edit the single view file: components/com_hotspots/views/hotspot/tmpl/default.php - there you can set a size to the map div.
And yes if you create a menu item for a hotspot, then the link in the popup leads to that page - and you can style this page individually. The problem is that if you have 1000 hotspots you will need 1000 pages
Ah, it just came to my mind that you should be able to use modules anywhere from Peter:
www.nonumber.nl/extensions/advancedmodulemanager
I haven't tried with hotspots, but in theory it should work.
Let me know if this help.
Cheers,
Daniel