I have played on my friend's Survival Realm for ~3 months and he was going to stop paying for the realm so I was wondering is there any way to get that world for my Personal Client.
Yes. First, click on the Wrench near on the right of your realm in the realm menu. Next, Click world backup and hit "Download latest." Once you do this, a percentage bar will come up and once you hit 100% you will be able to play the world in singleplayer survival.