Get the 1920x1080, that's 1080P, the 1366x768 is half the resolution and outdated. The heat and power consumption will be pretty much the same since with screens most of both come from the backlight and not the screen it self.
1) I believe there is still SOME increased power draw, possibly just due to the GPU itself processing more pixels but it's hard to guess since it depends on the hardware. Probably not too significant in a modern Intel iGPU.
2) No guarantee both laptops have the same battery life.
3) Backlight as said (AFAIK) is by far the biggest drain so adjust the Power Options so the brightness is the optimal balance of "bright enough" vs battery life.
4) By "heat" I assume you are referring to EXHAUST thus fan noise? I ask because the BACKLIGHT heat would have no effect on the fan that is mainly to exhaust the CPU/GPU heat.
true...power consumption will be the same but I think iGPU(Intel UHD 620) generates more heat with higher resolutions and since it is close to the CPU it can raise CPU temperatures which in turn can cause CPU to reach its thermal limit which in turn causes it to clock down....is that correct ? or the difference is not that huge ?
If possible I suggest you make a BACKUP IMAGE using a tool like Acronis True Image to make a compressed backup to another drive (probably a USB HDD). I'd wait until you are all setup (e-mail etc) and if you don't setup an automated solution at least setup a software reminder to periodically make a new backup Image manually then DELETE the older backup.
Acronis True Image isn't free for the automated solution but it does have a cool feature where you can add a USB HDD and I believe if you are past due for a backup it will then just startup and do it.
*Assume that your laptop drive could simply DIE at any given second and plan accordingly (or at least get severe software corruption you can't fix).
So to be clear you should:
1) manual or automatically make a compressed backup Image (i.e. Incremental)
2) setup a REMINDER if necessary (i.e. monthly to just plugin your USB HDD?)
3) create a BOOT USB STICK to initiate a RESTORE. For example if your HDD dies you would:
a) buy new HDD/SSD of sufficient capacity and correct size (some must be 7mm thick not 9.5mm if SATA)
b) swap new for old physically
c) attach the backup USB HDD
d) insert Restore USB stick and boot
e) follow instructions to RESTORE the backup to the new drive