First is rust all over the exhaust area
Second is on the right side of the motor where the dip stick is
Third in that same area there is a whole bunch of what looks like to me one of those "create your own gasket" deals because there is gasket material oozing out
First, congrats on such a nice mower; the HRX is a tremendous machine.
Second, everything you describe is 'OK' and absolutely of no concern.
(1) Exhaust is made of mild steel. It is normal for some surface rust, especially, as you say, in humid conditions. Tip: If you hose down the mower after mowing, avoid getting water on the engine, and 'burn off' any moisture after washing by running the engine for a few minutes before putting the mower away.
(2) The hole is threaded, and there's a bolt screwed into it from the underside of the engine. Should be visible is you peer down into the hole with a flashlight, maybe a gentle probe with a toothpick will reveal the bolt is indeed there.
(3) The two halves of the engine block (it has a diagonal split) are sealed together with liquid material called Hondabond; a physical gasket is usually only used for parts that may need to be pulled apart for service or repair, and statistically, it is unlikely the block will ever need to be cracked open.
Third, be sure you've registered your new mower with Honda to ensure faster service if you ever require any warranty work. Get the full serial number (MXXX-1234567) off the back of the mower deck, then register online here:
Click here to register your new Honda online
Finally, drop me a private message with a mailing address, and I'll get you some Honda stickers in the mail.