Question: Should I use MySQL with SSL protocol if my web application and database are on the same machine?

Answer: 
There is no definitive answer to about when you should use MySQL over SSL. If your website isn't dealing with sensitive information, then you most likely don't need it.

However, if you deal with information such as payment info (or similar sensitive info) coming back and forth from your scripting language and MySQL, then you will most likely *have* to use SSL to encrypt the information going trough the network. 

Even if you secure your script and your database, a person who has access to the network or the machine in question can sniff the traffic on MySQL's default port (3306) using `tcpdump` program, and therefore obtain all info going between your website and the db. 

If you need to comply to certain certificates, then you will be required to ensure MySQL over SSL because you have a potential security hole and if anything goes wrong, it can be used against you to blame you for misconduct.

If you have a simple website, then using SSL is simply an overkill and you can safely ignore it for the moment.
That depends on how much you trust the other users on that machine. If you don't use SSL, the logins will be passed as cleartext, and potentially sniffable by anyone else on that machine.