You cant trace it back to a specific date. It really depends on what you are willing to consider a "guitar".
To find out how old your guitar is you can check the serial number and go back to the manufacturer to find out when it was created.
Sometimes yes.
Born23 July 1965That would be almost 45 years old.
If it is a popular brand guitar often the serial number gives the info. Search for your brand serial number decoder on the internet.