Do I need to backup my data before replacing my hard drive? (mid-2012 MacBook Pro)

I would most assuredly not only backup, but make a clone of what you have that is bootable.

I think you'll find an additional drive is money well spent when it comes to trying to replace lost files or you have a dying HD..

Yes, you should be able to access your files from the external drive. That said, anything can happen so it never hurts to backup first.

As others have stated, backing up is essential. I keep both a Time Machine backup and clones. You can use a cloning software like SuperDuper! or CarbonCopy Cloner.

The advantage of the clone is that you can boot from it and use the system. So, if your hard drive fails you can just boot from the backup and keep on working until you have the time to repair or replace the internal drive. You can also drag and drop files with the clone because it is the identical file structure on your primary drive.

The advantage of TM is that it creates recursive backups, so you can restore a file or the entire drive from a certain point in time.

Even if you don't plan to replace your hard drive, you should be backing up your data on a regular basis. Your drive WILL fail sooner or later. It's not a question of if, it's only a question of when. Time Machine makes it brain dead simple to back up. All you need is an external hard drive.

You should be backing up your drive because the Sun rose this morning and will set in the evening.