Do you have a .htaccess file that is redirecting to https? You may need to remove that on your localhost to get it to work.
Whatever is redirecting from http:// to https:// is probably the root of the problem and has to be removed before you will be able to get Dreamweaver to connect to your database since you won't be able to get an actual SSL certificate installed on your localhost.
The redirect in IE could be a 301 redirect in cache... Perhaps clearing the cache would resolve that.
I'd work on getting Chrome to open with http:// and not automatically go to https://. Once that is working then try IE and if it still has issues try clearing the cache.