Both of those are centre-lock discs. The bolts you see are decoupling the discs itself from the spyder - don’t take these out. The disc comes off near the hub, look up centre lock.
Changing to a 180mm rotor means you’ll also need an adaptor to move the caliper out to accomondate the larger disc. As you already have two different sized rotors on the bikes (but on the same wheel), you should have one of them already. Regarding caliper, see if they are flat mount or post mount. Many people prefer a larger front rotor as the front brake takes more weight, especially down hill, but you can run two similar ones too, so I wouldn’t worry too much about it.
Talking about brakes (and assuming they are hydraulic) - you might want to bleed them sometime. You’ll need a bleed kit, basically just a few syringes and some stuff. There are two types of brake fluids in use, mineral oil (shimano) and dot 5.1 (sram), you need to use the right one and do not mix them. (If the brakes are a different brand, look up what they use. Magure call theirs “brake blood” and colour it red). Bleeding brakes is easy. You’ll only need to do it when braking feels odd - ie the lever feels “spongy”, or there’s too much travel or not enough. Also maybe if you change altitude by a lot or have the bike upside down for a long time. Look up brake bleeds for your type of brake on youtube.
Forgot to mention, get a stock of brake pads and learn how to change them. In the wrong conditions, you can go through a set in one ride.