A:AnswerNo, I don't believe it does. Hp made models that do but I'm not sure BestBuy sells them. This display is 1920 x 1080, which is the next step down from 4K.
A:AnswerBattery has averaged 2.5 to 3 hours under normal use and 1 hour or so with gaming (as should be expected in any gaming laptop, really). The RAM can be upgraded given you are patient and careful when you unscrew and pry open the back. 8GB of 2133Mhz RAM is what it has stock in one of the two available slots.
A:Answeractually yes you can. there is a single 8gb stick installed and a fully open slot. its pretty simple to remove a few screws from the bottom and carefully pop off the bottom then the ram slots are right there in front of you. not at all hard to do.
A:AnswerOf course it has wireless.
Per the specs, posted here: http://lifeinbits.net/wp-content/uploads/2016/06/15.6-OMEN-Laptop_Datasheet_BBY.pdf
as well as on the HP.com website
Network Card • Integrated 10/100/1000 GbE LAN (29)
Wireless Option • 2x2 802.11ac WLAN (19) and Bluetooth® (26)