First off just to make sure we are all on the same page, based on the model number you provided this is a 160 GB My Book Essential with a green ring on the front like in the picture below:
Considering how old the drive is (In my experience, the average lifespan of a hard drive (in use or not) regardless of manufacturer is about 3-5 years) the answer to your second question is an emphatic “Yes” - you should ALWAYS have TWO copies of important data on separate current devices. Some people recommend a “cloud backup” for the second copy, although I personally prefer to use a small “passport” drive and keep it off-site (in my case in a safety deposit box at my bank).
Here is a good low-cost desktop (wall-powered) drive that should work as the replacement drive:
As for the backup, you can use another identical drive, or if you want something more portable (easier to take off site) this one will work:
Total cost of both drives would be around $150 USD + tax etc.
As for your first question, the first thing we need to determine is if the drive is still functional. While the drive you are using is not officially compatible with Windows 8.1, the OS most likely will be able to detect the drive out of the box. We use Microsoft drivers for our externals for this (among others) reason. To do this, power up the drive and connect it to your computer’s USB port.
If the drive is recognized, you are good to go - copy that data off ASAP and ensure you have two copies. I’ve seen cases where really old drives like this work for a little while and than fail after a few hours of use so I would do the copy operation ASAP.
If the drive is not recognized, please reply back to this thread and we can continue to diagnose the issue from there.