1) if I save a picture from Safari or Mail app, is the quality reduced? Can you rename pics once they are saved in photos app?
Full quality. You can't name photos (in fact, you can't even see the file names) but you can create albums with names and put photos in them.
2) can you share a video or other media via Bluetooth or Wifi direct?
This is where "There's an app for that" comes in. The OS does not send files, you've got to figure out what system or service you want to use to share files.
Dropbox works over the internet. Things like
Documents Pro can copy files over USB to any computer with iTunes on it. There are possibly bluetooth solutions but it would involve the same app being on both phones...I've never tried that so I don't know.
3) can I save songs from my friend's computer to my ipad without deleting songs already there in my library?
No. Well, not in the official 'music' app, anyway. You can use other programs like Documents Pro that I mentioned up there. That will work, but it's more of a file-browswer than a media player so you'll find the controls less than amazing.
So there are solutions, but if you really want music on your phone you mostly need to copy it on to your computer and sync it using your iTunes. (Remember, you could use a USB app to copy the files and bring them back to your computer, but at that point I'd suggest copying them into iTunes and then syncing them, rather than trying to play songs out of a file manager.)
4) can I save an excel file locally and send it to someone else? Can I save any file / media locally that I receive in mail.
When you get a an attached file in mail you can 'send' it to various apps installed on your phone such as Dropbox or iBooks and so on.
It depends on the file type. For example, PDFs will show you the kindle app as an option, Excel will not. Both will show Dropbox. So you'll need to find an app you want to use with the file. I see that
Numbers lets me open an Excel file on my phone so that's probably a good choice. I also see that
Smart Office 2 works too, but I haven't used that as much so I don't know which is best to use.
The point is, "there's an app for that" is more than a catch-phrase, it's also instructions for how to make your iPhone do what you want.