Day of planner?

Yes, since a day of coordinator also does a bunch of other things in addition to setup and tear down: they keep the timeline on schedule, be the contact person for vendors when they have questions (such as, where to setup, or accepting deliveries of flowers/cake/rentals/etc), reach out to vendors that are running late, inform venue of any issues that arise and ensure that they're resolved (bathroom runs out of paper towels, guest spills drink in the middle of the dance floor, dessert bar runs out of plates, etc), cue the DJ on when to start/stop the first dance/parent dance/bouquet toss songs, make sure that whoever is giving a speech gets the microphone at the right time, making sure the caterers are ready to serve dinner on time, etc. They handle all these tasks so that you don't have to, and so you can instead spend your time socializing with your guests, dancing, and celebrating your wedding!

Yes, I recommend one. Those things are not a Day-of coordinator's duties, although mine will assist with setting up decor that I provide like the guest book, pictures, etc. The DOC is the main contact with all vendors, answering all questions... There's just so much that needs to be communicated and done. You don't want to be stressed out about it or make your family stressed. Here's a screenshot from my DOC's website that might help you decide.

Yes. I recommend one. They take care of many other things like others said

I'm going against popular opinion here and saying probably not - my venue sounds similar to yours and included an "event planner" who was our point-of-contact for all things prior to our wedding and a "day-of coordinator" who worked the actual event. The event planner helped us develop our timeline, choose linens, create our floorplan, was the point-of-contact for vendors, etc. and the day-of coordinator set everything up (including all the décor I provided), timed my wedding party for walking down the aisle, packed up all our décor at the end of the night, etc. I asked a million and one questions about the day-of coordinator's responsibilities ahead of time, though, just so I wasn't stuck, for example, having to set up all of my DIY centerpieces. Long story short, just ask your venue what the day-of coordinator will and will not do and decide from there!