Lap tops

Hello, I'm planning to buy a new laptop at Christmas, the main use for it will be for application development and few games from time to time, my main concerning will be its performance, battery lifetime and not less than 15" screen, I want something may last for 4 or 5 years without changing...

I am thinking of buying a laptop with 16gb ram 526gb ssd and i7 but I can't think whether to choose 6 cores or 4core or8core.Will a quad core laptop be good for running Android studio smoothly as it will save me some money

It's been a few months since my laptop Toshiba satellite L755 (i know quite old) restarts really randomly, when I'm on YT, simple search, just logged in my account or even the windows logo showing, i thought it's ram but no ram is fine since i ran memtest for 24hrs with no heating issues too...

I have lenovo g70-70 laptop. My laptop have one jack for mic/speakers, but my headset have two plug (one for mic, one for speakers). I m bought splitter something similar...

Looking at two laptops, both Acer both to run Windows 7 - do not want window 8, and both the same price. Not a computer geek, will use as a basic computer for internet, some brain training for my husband who has a brain injury and some word processing. Which would be a better computer for me?