It is not possible to definitively answer the question basing on the problem description. The data may already be overwritten or maybe not. You should download and try DMDE Free Edition. Read first the installation notes.
You are using Free Edition: you may recover files from the current panel only (currently visible files in the opened directory, up to 4000 at a time). Make sure not to mark directories or files in other directories (use context menu, e.g.). Or buy a license and make sure you are using a licensed copy.
Yes, paid editions recover preserving directory structure shown in the tree panel. However you should first try file recovery with Free Edition since file contents may be damaged (see the next question).
Make sure you tried the most recent software version. Run Full Scan, try opening different volumes and reconstructing file system and data recovering. If you still have problems then files are probably overwritten after removal (for some reasons) or file system is damaged seriously. Not overwritten files of known types may still be recovered using signatures without original names and directory structure (see the directory "Raw Search Files by Signatures"). If DMDE does not support necessary file types you may try other software or address to specialists. It may also worth trying the most recent beta version for the newest features and fixes.
No, the main rule of data recovery is to not write anything to the damaged disk. Automatic fixes may cause irrevocable data loss. Human study is required before any such fixes. Anyway you need another medium to keep a backup copy if your data have some value. DMDE is a data recovery software and not a file system repair tool.
If you have a backup copy, you can try the built-in OS tools, such as chkdsk on Windows and fsck on Linux, they fix FS errors (however data deletion is possible).
Make sure you completed the order and specified correct email address. Check your spam/unwanted mail folders. Request your license key. If you don't get any responce then your mail server is blocking incoming messages / not working, in such case feedback us providing your order details and another contact address.
Make sure you are using an original unmodified software copy. Download the software again from the official site, unpack, launch and enter your license key.
Request your login if your license support is not expired.
You may find upgrades and discounts available for you in your personal site section (restore login).