does external backup continue when my mac goes to sleep

Hi Ubetican,
That is a good question about your external hard drive on if the drive stops when your MacBook Pro goes to sleep. The answer is that it may depending on settings. You do have the option to have your computer "Put the hard disk(s) to sleep when possible" and it also depends on the external hard drive as well. I can't speak to those drives on their features, but I would check in System Preferences > Energy Saver to look ever your settings to make the choice that you are looking
About Energy Saver sleep and idle modes in Mac OS X
https://support.apple.com/en-us/HT201714
Have a good day