Is attaching a database on the same server under a different database name possible? I recently offered to help a friend with some development. She isn't a technical person and it turned out what she needed was more a DBA/SQL developer. She gave me the IP and password to this server.

There is no development server. Only production. So I have to be extra careful with everything I do. 

I accidentally altered a stored procedure and now I'm trying to get it back. I had the old employees send me the lastest files. They were in rar format and after I unzipped the DB folder, there was only a file inside(no extension). Looking at the contents led me to believe it is a SQL Server .mdf file. This leads me to my question.

Can I attach this mdf file to a new database I just created? Without it trying to take down the other instance? It seems like I could but since this is production, I have to be EXTRA careful.

The server is Windows Server 2008 R2, with SQL Server Management Studio 2012 installed.
You can first check to make sure it actually is a valid MDF file using DBCC CHECKPRIMARYFILE. It is an undocumented command but can be useful at times.

If that turns up nothing or shows that it is not a mdf file you can use the RESTORE HEADERONLY to see if it might be a backup file.

To your specific question, yes you can attach this as a different database name as long as the physical file is not in the same directory on the server as the original. So in your case I would just create a sub-directory in your data folder for this file and the future LDF file that would be created.