If you plan to sit very close to a 43" screen, then you are going to run into issues at 1080p, the pixels are easily visible on a 27". 4K 43" should be okay at around 100 PPI.
27" 1080p = 82 PPI
27" 1440p = 108 PPI
43" 1080p = 51 PPI
43" 4K = 102 PPI
Retina ~= 300 PPI
IPS / PLS - These days, response times are pretty good for monitors and okay for large TVs. Great viewing angles. Generally good color accuracy.
VA - Fast response times, decent viewing angles (Why a lot VA gaming monitors are curved, to get the best viewing angles).
TN - Faster response times, poor colors and viewing angles
QD-LED (Samsung) Your QE43Q60ABUX would qualify. Great colors, poor viewing angles, (apparently motion blur issues according to RTINGS (I have a 32" version of this)
OLED - Fastest response time, great viewing angles, excellent colors, perfect blacks. Extreme cost and durability is still an unknown.
There are more technologies like QD-OLED, and LG's WOLED screens. But they are all still on the pricey side.
If I recall, my main TV is a VA panel from Vizio, I don't find the viewing angles to be all that bad. A little off at the extremes maybe.
Yes, that is how games and displays work. You run your desktop at whatever resolution, and when the game launches (in full screen mode) it will send that resolution to the TV instead. The TV or Monitor's scalar will take the incoming data, make a best fit approximation of the color the pixels should be and use every pixel on the screen. If you run it in a window, then it will take up only that portion the screen as compared to the resolution on the desktop.
I don't know what you mean by fully convert, you can't force a display that has a fixed number of pixels to display anything other then those pixels. Without rescaling, you would end up with a 2560x1440 image with black bars on 4 sides, it would be roughly 66% of the total area. At 43" that would like a 28" display.
Complete detail on how the image gets displayed is best answered by external sources.
Very simply:
Game Engine <-> CPU/Storage/Memory -> Video API instructions -> GPU -> (A WHOLE LOT OF STUFF) -> Signal encoding -> Display Output -> Display Input -> Scaler/Processing -> Signal Decoding ->
LVDS (Low Voltage Differential Signaling (basically using a few wires to connect to all the pixels, kind of an addressing system) to set the color of each pixel. And while that is happening you will also have audio decoding.