I want to buy some fenders, and I've watched a few youtube videos about how to install them. I'm still confused as to whether fenders would work, and if so, which ones to buy. Here are some photos of the bike.

Yes, but you will probably need either P-clamps or to rig something up using zip ties. It's certainly not a huge deal, but it takes a bit more time then might otherwise be the case. I recommend and use Planet Bike full coverage fenders.

With disc brakes and a suspension fork you may have some difficulties with traditional fenders. Google around and see what is advertised to work with that. Alternatively, I'd recommend you post on the MTB forum.

Take a picture of the "bottom" of your fork so that we can see if you have eyelets or not. Also, take a picture of the bridge on your seat stay directly from behind, so we can see if there is a hole there to accept a bolt. If you have these last two things, it will be a simple and straight install. You already have a rack mounted into eyelets, so you're half way home.

I'm pretty sure these would work without too much trouble. They are compatible with bikes with disc brakes, you don't need fender eyelets, and they should work just fine with a suspension fork, just use black zip ties instead of the included rubber straps for security and to fit around the fat fork legs. Also, they are essentially full fenders, a little shorter than some maybe, but better than cheesy clip-on "filth prophylactics" and certainly better than nothing. Good luck!

Cheers
lverhagen

Good call. Never saw this model – and I have PB Cascadia fenders on my Cross, and Hardcore ATB on my Xtracycle, so I haven't looked in a while. Is this new? Anyhow OP, here's the mount instructions. (Just out of curiosity though, still take those additional pics if you can. You could have even more options.)

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Yup, PB Speedez are the best bet for the OPs set up. I have a set on my commuter. Easy set up and trouble free since I put them on a couple years back.

yes

Show a pic of the rear brake assembly, this is the tricky part of the rear.
usually you can fit a std bolt-on fender to the rear but need a clip on fender for the suspension fork. No-one makes sets of this kind so you either buy 2 sets of fenders OR use clip-ons for front and rear.

I have PB Speedez on two bikes and they work great and are easy to install. No problems with disk brakes or front shock.

back of the fork , if there are a couple threaded holes , at the LBS Here,
they have used that to mount the struts, pointed outward ,
then bent back to the line towards the strut clips on the fenders themselves.

Here are the additional photos asked for. The first two are the front wheel, the last two are the back.

Looks like a straight fender install bud. Get any kind of fender you want (appropriate width of course). You have fork eyelets for fenders and a reflector hole. And I see a hole in your seat stay bridge, and then you share your rack eyelets. I'm not seeing what you got around your bottom bracket, but it's obvious this bike was made with having fenders and rack in mind.

How do I determine what width I need? Is it based off the width I measure of the tire, or is it written somewhere on the tire?

I tend to go with a minimum of 5mm wider than the widest tire I'll use. Optimally I aim for 10mm wider for 5mm clearance all around. Gives good rattle room for pebbles so things don't get jammed up in a tight clearance, and allows for good deep cover over the tire to avoid side splashing.