The easiest way to play mp4 files is to import them into iTunes on the computer and then sync them.
You can sync some stuff with Microsoft Outlook using the Info tab in iTunes when the iPad is connected. I don't recommend it. Instead consider syncing both Outlook and the iPad to an online service like Google. It will work beter with less hassles. Can't help you with the Outlook setup (though I know it can be done), but you can set your iPad up with Google for contacts and multiple calendars using this method.
Setting up Google Sync with your iOS device : Mail, Calendar, & Contacts - Google Mobile Help
Safari is limited in what type of files it will reconginze. It will not work with download links unless it recognizes the format. When it does recognize the format, like a pdf, it will open it for viewing in Safari. Tap in the middle of the page and you should see a share icon at the to right. Tap on that and you'll see (probably) and Open In option. This option will list compatible apps that the file can be opened and saved in.
For general downloads from the web a good app is GoodReader. It has a built in web browser that can be used to download files, or you can enter the URL of the file directly. GoodReader will download just about anything, and view several formats. For formats it does not support for viewing you'll have to go to the app store and find something that will, at which point you will need to use the Open In option (available in most new apps) to copy and open the file in that app.
The iPad does not have a general files system that all apps can access. Instead each app has it's own file directory. To move files between them, you use the Open In feature which copies the file to the new app and opens it.
It is a different way of working with files, more secure, but it takes a little getting used to.
