I've been researching this a lot and it seems I'm the only one with this specific issue with my Raspberry Pi on my Wi-Fi network.
As I speak I have just reinstalled Raspbian Strech onto my Raspberry Pi 3 for the fifth time. You see, every time I reinstall Raspbian Stretch and then connect to my WiFi, my network will be fine for a certain amount of time. But then all a sudden, if I have to reboot the Raspberry Pi via unplugging and replugging or I just leave it alone for half-a-day, then every device I own will say it's connected to the internet, but then lose access to DNS servers causing everything to basically lose internet access - even though it says I still have internet access.
Now what's strange about this, is that it affects my router on the local level too. So it comes to a point that I can't even Remote Desktop or SSH, and I think the same would happen if I remote into my other Windows devices as well. This is a very strange phenomenon and to my knowledge, again, this is only happening to me.
At first, I thought that it was a simple screw-up in my router, but then I discovered that indeed my Raspberry Pi is a direct cause as soon as it connects to my Wi-Fi. So then I was researching the limit on how many devices the average Wi-Fi router can handle. Thinking that I would have to upgrade my router. But then I come across articles like this that say the average Wi-Fi router can handle up to "250 connected devices" wirelessly, and four wired.
So what gives? Is this the Raspberry Pi's fault or is it my router? Back, in the beginning, I only installed Ubuntu Mate because I preferred Ubuntu, but then only my desktop couldn't connect to the internet, but that was fixed when I connected my desktop to a VPN and then the connection reset.
As far as I can tell this can't be fixed by commands such as "winsock reset" on the command prompt. I've tried multiple times, even calling up my ISP when this first happened. It's important to note that, even though the Raspberry Pi cannot handle it - and I do not think this is the trigger - I use my Raspberry Pi to make a Minecraft PE server. But if this was the trigger, it would lose internet access almost immediately. But when I first tried this it stayed up for hours. So maybe there was no point in bringing that up. But it's necessary to tell you everything I'm doing to diagnose this issue.
So, is this a problem with my router or Raspberry Pi? The version I'm currently running is "September 2017" (why is there no version number?), the latest as of this post. And the connection is wireless, not wired, as I ran out of ethernet cables. And my desktop is the only device wired to my router.
The type of wireless router I have is a Netgear "N150 Wireless Router WNR1000 v3."