1366x768 is the resolution of the monitor/laptop screen. And usually when you increase the resolution, things will look better because you have more pixels to fill stuff in. But it also means you need more power to play at the same settings.
I see you have increased the resolution to 1080p, this will mean that you probably have to turn down some settings to play smooth in 25 raids. But I dont have enough experience with the new laptop CPUs. But you should be fine, and otherwise just turn down some settings. Thats not the end of the world
Small sidenote, your gpu is still the 750 and not the 765.
As for an external monitor. Be sure it has the proper connections. The laptop probably has a hdmi out, so your monitor should have that aswell. And than you have to decide for yourself if you want ips or tn
IPS: better image quality, better viewing angles, lower response times, and could have some input lag
TN: Lower image quality, lower viewing angles, better response times
(These are just short pro's and cons for both. There are some threads going around about IPS vs TN. My personal preference lies with IPS.)