You can copy all of the files, but most are not needed for the average user. bitcoind and bitcoin-qt are the main binaries. They are each self contained and do not rely on each other or any other files in the release.
/bin has all of the executables. Besides bitcoind and bitcoin-qt, bitcoin-cli is the only binary that might have meaningful changes between releases that you'd want to also copy it over. But generally, it's fairly version agnostic. The other executables in /bin are just utilities and the unit tests which are really only interesting to a very small set of people who probably aren't asking this question.
/include and /lib contain files for libbitcoinconsensus. If you don't know what that is, you don't need those files.
/share has manpages and a script for generating rpc credentials, most people don't need these either, unless you like using man instead of -help.
The easiest way to install is to just copy the folders into /usr, and do the same for every upgrade. That will copy every binary over, and also overwrite any existing binaries with the new version when you upgrade.
You can follow the above steps if you feel you need the current version of the core.
In simple terms just back up your wallet and configuration and a copy to a safe storage.
Close your Bitcoin core application to prevent it from running during installation
And then install the current version.
which is poor connection, or should I say: poor service from my ISP.
It is. Since you are from Nigeria, I think you might be using Glo.