Reddit mentions of ZTE Axon 7 (Grey) Unlocked

https://www.amazon.de/gp/product/B01I092IPC/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
Was a bit more expensive than when I bought it, EUR 380 seems pretty reasonable!

I don't really know since I live in US.
You can try and buy it on Amazon.
https://www.amazon.co.uk/ZTE-Axon-7-grey-unlocked/dp/B01I092IPC/ref=sr_1_1?ie=UTF8&qid=1498180038&sr=8-1&keywords=Axon+7

You can try eBay but the seller is from China, so you are expecting a long wait. Not sure how reliable it is getting it shipped from China.
http://www.ebay.co.uk/itm/Unlocked-5-5-ZTE-AXON-7-Quad-Core-4G-LTE-Android-6-0-Smartphone-20MP-Dual-SIM-/232240934359?var=&hash=item3612a36dd7:m:mRZKUzAJCTRCM8ImY_mNEQg

Either way, it is under your max budget. You can wait for newer phone to come out if you are interest. There is newer Axon phone but not sure how well it would. It is up to you.

For me, I am just simply happy with my ZTE Axon 7 for its price and performances.

Edit:

Forgot to answer your last part.
Well, the "4-6 batteries on screen" is basically where it allows you to monitor how long you have been using your phone while it is on. I don't mean like playing some music and turning off the screen then go on your day. It is more of like you are constantly using your phone non-stop like browsing reddit. Someone can correct me if I am wrong but that is what I believe it is. Of course, you can't really check it on your iPhone because Apple didn't really allow it or something with their battery monitoring app. For Android user, I believe some of us use GSam Battery Monitor.

https://www.amazon.co.uk/dp/B01I092IPC/ref=cm_sw_r_cp_apa_qUVXAbGQZQ1N4