Yes just about any external USB drive should work. I am using an LG GP60NB50 drive, you should be able to get one of these for $35 or less. It looks good (black, also available in silver), is extremely portable (only 14mm thick), it's quiet, and has some other interesting features such as support for M-DISC archival media.

I have several external drives, any drive with a USB connection should work.

everything now available in internet, if you want u can use ex-DVD drive ( without power cable) or use desktop or other laptop which is have dvd and share over the network or copy through thumb drive.... now a days by practically usage of dvd is very less and some people need who mostly watching videos... upto me its not a big deal

This laptop is around 7 years old, you may not be able to fix it