How can I download a file using Internet Explorer (or any other browser) on Windows Phone 7.5 Mango, and save it to my phone. Currently it just opens the file. Is there a way to save it instead?
You cannot download media files using the browser. The browser will only allow you to stream them and will not allow you to save them to your media library.
You can download Office files, text, images and Zip archives (as long as the archive contains supported types).
Well I Have found a software that can download videos for u which MediaDownloader Here is the link for that http://www.windowsphone.com/en-us/store/app/media-downloader/d5484913-8bfd-477a-bc96-b3aa2e9dcee1
Now with Windows Phone 7.10.8XXXX u can even transfer files via Bluetooth.
You can download any file using UC Browser also you can share videos, music etc through bluetooth also .