Grats!
The deck probably isn't adjusted properly if the tires were still at shipping pressure, so don't freak out if the cut quality isn't up to par. I really hate that dealers do that! You'll likely have to adjust the pitch and level yourself.
The whole deck is offset to the left to increase overhang and trimming ability on that side. I suspect that has something to do with the front caster placements.
I keep the hydro fluid a little high in my machine as it's difficult to see if it's at the full line which is very low in the reservoir and hard to see. With it a bit higher I can check at a glance.
The deck adjustment procedure is in the manual. I haven't adjusted the deck on my Bob-Cat so I don't know that procedure. On my Exmark Z I loosen the chains to drop the deck on precision thickness blocks, then tighten it all back up. Varies by manufacturer and deck. In general you want the deck lower in the front by 1/8 to 1/4 inch. That's known as toed. For my Bob-Cat Dura-Deck they say it cuts best level, but my dealer sets them up with the back slightly lower (heeled) and I've left it that way. You end up cutting each blade of grass twice, which is great to eliminate missed blades of grass, but it requires more power and can lead to discharge/clumping issues. It's generally not advisable. It really all depends on your particular cutting conditions and the characteristics of your deck, but healing isn't the norm, toeing is.
You may also have an adjustable front lip. I can't recall if the CRZ has that. Again that depends on cutting conditions whether you run it up or down. It's easy enough to experiment with.
And yeah, that's why I fill my reservoirs a bit over the fill line. It's just an expansion tank so I just run it 1/2 inch or so above the line where I can see it. Not going to hurt anything and still plenty room for expansion.
The mower should have come to you ready to mow and it appears that it really isn't. Sadly that's pretty common. You can mow with it with the pitch off until you get to adjusting it, but your cut quality will likely suffer.
I know you said that your lawn is fairly level, but just a word of advise on operation. Z mowers have control issues going down slopes because the weight of the machine shifts to the front wheels which you have no control of. To maintain traction and control on slopes, operate the mower so that you maintain weight on the rear wheels.
Expect to rip the lawn up a bit on turns, especially at first when the tires are brand new and "sharp" and you're inexperienced on it. It's just like pushing a heavy shopping cart, the way you push with one hand and pull with the other. A lot of inexperienced operators "one-stick" their turns which causes the inside tire to pivot while stationary and cause turf tearing. The proper way is to separate the sticks on turns...as soon as the inside tire stops going forward it should be reversing. Some people never get the hang of it or just do 3-point turns.
If you find the ride is still too harsh you can add the suspension seat base.