Have no experience with number one, but I can answer some questions about the rest.
Note that all of these apply only to the ZE552KL "vanilla" model of the Zenfone 3 - that's the one with the glass back and the 5.5" screen. Other Zenfone 3 models (including the Laser, Max, Ultra, Deluxe and Zoom) may be different.
Try to restore the Android Message apps to factory default by unistalling it from the play store and then disable auto update for that app (via the 3 dots un the upper right corner of the screen).
https://play.google.com/store/apps/details?id=com.google.android.apps.messaging
I've had this problem just after the playstore pushed an update that enabled RCS in the sms client.
My phone was unable to charge when plugged in a usb 2.0 port of my pc and also some discharge occured when the screen was on, even in idle. After restoring to the factory Android Messages and rebooting, the phone returned to the normal charging behaviour.
The battery drain should only happen if the carrier support the RCS protocol (ex: Vodafone in Italy), my brother have the same ze520kl but with h3g carrier and his phone have not suffered from the drain.
I had the same problem, super annoying. I got rid of them by installing this app https://play.google.com/store/apps/details?id=com.iboalali.sysnotifsnooze it works well, haven't seen one of those notifications since.
I got these from Amazon:
https://www.amazon.com/ZenFone-ZS550KL-Dretal-Premium-Frosted/dp/B01N3L2935
And I am very impressed with the clear one, it has like an air cushion all around it, at first I was like "it could have been smaller so it was tighter" but later paid attention to why, I really like this case as it shows this beautiful phone quite clearly (pun intended, lol).
Confirmed received from Amazon.com just this past Monday. The one in the link: https://www.amazon.com/ZenFone-5-7-inch-Unlocked-Warranty-ZS570KL-Glacier/dp/B01LQV1YU6/ref=sr_1_2?s=wireless&ie=UTF8&qid=1476999076&sr=1-2&keywords=zenfone%2B3&th=1
It's 5.7" model ZS570KL only comes in glacier silver from Amazon.
ASUS ZenFone 3 Deluxe 5.7-inch 6GB RAM 64GB storage Unlocked Dual SIM Cell Phone, US Warranty (ZS570KL-Glacier Silver) https://www.amazon.com/dp/B01LQV1YU6/ref=cm_sw_r_cp_apa_-YMcybKAWFSAE
Video of it in action: https://streamable.com/tnfuc
This follows after Sony, who integrated the Google Now panel into the Xperia Launcher in June of last year. It works on all devices, too, not just ASUS devices. It's not my personal favourite launcher, but it has some nice qualities and it's definitely worth a look.