How to restore deleted items from the Ubuntu trash?
If you delete a file from the trash (or delete it without even sending it to the trash, like with shift+del or rm), it can't be recovered. Technically, the data may be there somewhere on the disc, which you may get back with reading the disc contents directly (which is a Not Easy task, but theoretically possible if you deleted some very important data; but very important data should always be backed up), but it is quite possible that it is already overwritten. So I can say that practically your data is lost. It is because the structure of Linux file systems.
Note that on the other hand, it is possible to recover deleted files from Windows partitions (like FAT32 or NTFS), and there are several tools for that. But the data still gets overwritten pretty quick there, so it is practically impossible to recover a deleted file from a Windows system partition.
That's exactly why the concept of a trash is invented, to prevent users accidentally losing their data. If you tell the computer to delete something from the trash, then you must be pretty sure you want to delete it.
Here is how you can add Trash icon on desktop. After adding this icon it is very similar to Recycle Bin from Windows.