No,
you cannot do this because your phone does not have a recycle bin.

This is absolutely ridiculous. Recovering data does not mean restoring from the recycle bin. The data can most certainly be recovered (but that depends if you've rewritten the storage device). Just search for proper data recovery software (mention for memory cards). Try TestDisk

Yes you can! As long as the phone is visible to your computer as a Windows drive, then you will be able to scan the phone's drive, using a third party file undelete utility. File Restore Professional will get your lost files back. You can donwload a free trial at: www.pcrecovery.com

Yes you can..

(i) Using the *#7780# sequence.

It will restore ini files from ROM keeping all your data (themes, 3rd party applications, video, photos, and music files)

(ii) Using the *#7370# sequence.

Completely format phone memory. Default files are cleaned up and rewritten.

Note that data found on memory card will not be altered

Note: When using symbian60 v1 based phone such as nokia 7650, 3650 or N gage models these two key sequences can be entered in the same way you dial up a phone number. The phone will prompt you to enter a security code (12345 by default).

On the latest S60 phones you can try a Deep Reset, using the following steps

Turns off the phone

Press simultaneously on the green/talk, 3 and* keys and hold the 3 keys.

Turn on your phone

Wait for the onscreen Format message then can release the three keys

This method may also work for Nokia phones that won't turn on.

Note that before making a reset on Nokia's latest phone (N96),using the *#7370# or the 3 finger method, better make a backup, as you will automatically delete important data:
The license for pre-loaded contents (music, video, maps,etc..) and pre-installed application (N-gage).
Better use this method (reset) as a last resort.