First time to install Clincher Tire to Rim
Congrats on taking the first step to DIY.
Rim tape is used to make sure the inner tube does not get punctured from sharp edges where the spoke connects to the rim. Also, if your wheels are rim brake alloy wheels, Rim tape can act as thermal insulation to protect the inner tube from exploding under extreme braking. Since your wheels are Carbon and if your wheels do not have any of those spoke edges exposed in the rim bed, then no you do not need it and it would be just additional weight.
I suspect perhaps those wheels may have something already in place that makes the inner portion smooth and thus would make rim tape redundant. It never hurts to call customer service too to double check, but if you are not seeing an exposed connection point for each spoke, then you probably are good.
Regarding installing a new tire, I would say take your time and have good pair of tire levers. These videos should help

                
            

                
            
The hardest part is near the end when lifting the last portion of the bead into the rim. Note the technique Calvin/GCN uses with the levers as that is the correct way to use them. Also as a side note that was the easiest I have ever seen a road tires slip over a rim in these video. I ride on Continental GP 5000 clinchers and the last part of the bead is not usually that easy to lift over the rim (i.e. expect to put some force to lift the bead into the rim bed), which in my opinion is a good thing.
Also, after you are done mounting the tire make sure you inflate it and ensure the bead + tube is inside the rim all the way around. Oftentimes, I will inflate the tire to max rated pressure on the 5000s that is like 110 psi for a 28MM and that forces the bead into the edges of the rim. After that I reduce pressure to what I ride on and that should be it.
Of course make sure you put your wheels on the bike properly using your quick release, etc.
Wear your riding glasses or a pair of safety glasses (my pref if I do not have a flat on the side of the road) just in case a tire lever or something goes flying accidentally or snaps.
Hope that helps.