When I try to open my drawing, I get a message that my drawing needs recovery.

This one is easy.  AutoCAD has detected some anomaly in the drawing.  Instead of trying to open it, select the Recover command.  It works just like Open, but does an audit on the drawing.  Usually, AutoCAD determines that nothing is really wrong and you can go on.  If it does find something amiss, it will attempt to reconstruct the data.  If it is too badly damaged, the data will be deleted.

Every time I try to open my file, I get a message that says Fatal Error.

The patient is dead. If you're prepared, you can rename the .bak file that is made every time you save your drawing (provided you didn't disable this feature).  You can use Explorer to rename the .BAK file.  Let's assume your drawing file is named PART.DWG.  There should be a file named PART.BAK in he same folder as the drawing.  Rename it to PARTBAK.DWG. 

Hint: You can't rename it to PART.DWG because that file already exists.  You could also look for the autosave file and see if it is newer than the .bak.

So, you're unprepared.. there is no .bak or autosave file.  You'd better hope there is a backup of your file. If you didn't just start your drawing today there may be a backup of your work.  Is a tape backup performed on your computer or your network?  If not, you're in trouble.  If so, track down the person responsible for setting up the tape backup. 

The process for retrieving the file depends on your particular device and the software it uses.  If you use a mass storage device, like a Zip or Jazz drive by Iomega, retrieving files is just like copying files in Explorer.  If you're using a tape device, you must use the tape device's software.  Information on tapes is compressed and stored in special file formats.

When I try to open AutoCAD, I get some crazy message about maximum number of users reached and AutoCAD ends.

This problem tends to be associated with AutoCAD r12 and is related to something called the password file.  The password file believes another AutoCAD is currently being used and won't allow you to continue until it becomes free again.  The problem is that AutoCAD not being used by another person.