The current WiFi card installed, Killer 1435, makes the usage of internet very difficult. I want to change to a Intel 8265, but I saw that the card is soldered into the motherboard. Is there a way to get the replacement done even though the card is soldered?
You cannot change the card on the motherboard but you can add a usb network adapter and disable the on board card. But consider this- the Killer is an A/C adapter that is the fastest now so you should have an A/C router. If you don't have a/c wireless router that could be your problem. They are pricey.
https://www.lifewire.com/802-11ac-wi-fi-wireless-routers-818077 Consider upgrading the router.
I don’t recall ever seeing the 9370 available with Intel WiFi as ejn63 mentioned, but there’s no option for replacing it short of replacing the entire motherboard. However, Killer has been acquired by Intel, and I believe (but am not certain) that the Killer chip in the 9370 is just a rebadged Intel chip with the extra Killer software. So if you haven't already, try uninstalling the Killer application/“enhancements” so that you just have a basic driver. It might improve things.
Since you do not mention what your exact problem is with the network connectivity, maybe a couple of questions about that.
Do you have you wireless router set up to use different SSIDs for the 2.4 GHz and 5.0 GHz networks?
How many external antenna does the router have? This questions relates to the beam forming the Killer card performs. There is also something mentioned about "Wave 2" which is a newer Wi-Fi technology.
Folks in other threads are complaining about the fact the wireless will not reconnect after coming out of low power mode. This may be related to a router if it is older. If it is older, you might want to check for a firmware upgrade for it. My router is only two years old but since I now have an Intel Wireless-AC 9260 card (Killer 1550), it is even out of date. So Mary may be on the right track.
I can see what you all mean in terms of the router, but I will be heading to college in the fall and won’t need to worry about a single router. Would a external USB wireless adapter, as mentioned above, be a practical solution to account for both networks (5.0 GHz and 2.4 GHz)?
A USB WiFi adapter isn't a great idea. The ones that are just tiny USB dongles will never have range as good as built-in WiFi from roughly the same era because built-in WiFi uses large antennas within the display bezel, whereas a USB dongle has to package everything into that little dongle. The only exception would be USB adapters that themselves come with an external antenna array "pod" that connects to the USB adapter with a cable, but obviously that's a lot less portable.
To the point made by @Saltgrass above about not reconnecting, I've been seeing that behavior on my Intel 9260 WiFi card (and on the Intel 7260 I had before that) ever since updating to Win10 1803, so I'm hoping that gets resolved with a driver or OS update. In my case, I notice it when rebooting my system. Sometimes it connects right up, other times it sits disconnected for several minutes first.
I now see the problem with a USB adapter, but still don’t know if a solution to frequent wi-fi disconnecting. The change in router makes sense, but I won’t have much control over that. Any suggestions that would fix the problem of the wi-fi network frequently being lost even though I was connected to it?
Are you seeing this frequent disconnect behavior with one particular router, or have you observed it with multiple routers? If it's just one, then I wouldn't automatically assume that this card will be a problem with other routers. But in terms of suggestions, have you updated your router firmware? And did you try updating the Killer drivers and uninstalling the "enhancements/application" as I already suggested above?