Q: iPhone 6 - 9.3.4 update issues

Did you perform the update OTA using the phone, or using iTunes? Standard user troubleshooting steps are restart, reset, restore from backup, restore to factory; testing after each step. You have done the restart, so here are links for the other three. A reset is now called a Force Restart in the first link.

Restart your iPhone, iPad, or iPod touch - Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

if the phone is under warranty call Apple

http://www.apple.com/contact/

if the phone is out of warranty contact them as well and see if they can schedule an appointment at Apple Store

shortage of battery is something I'm seeing in my old 4S but not rebooting or instability.

you may consider resetting the phone

Recommended settings for Wi-Fi routers and access points - Apple Support

however this first method will delete your data

if you backup with iTunes you can restore your data later

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support