I have a Lumia 650 with Microsoft Windows 10 Mobile system and have problem install extract .exe files. I also cannot install any virus program on it like Avast. Please advise.
Although the core parts of Windows 10 ("Win10") and Windows 10 Mobile ("W10M") are mostly the same, the parts that interact with user programs are very different. Win10 includes a lot of legacy functionality to run existing Windows apps (such as Avast, or Firefox, or Counterstrike). W10M doesn't include any of that. Additionally, W10M only allows installing sandboxed applications, which cannot access most files or interfere with other programs; even if you could get Avast (or any other antivirus) into and installable W10M app bundle and convince it to run, it wouldn't actually work because it wouldn't be able to access any of the stuff it needs access to in order to work. Finally, you wouldn't actually be able to get it to run, because Avast is distributed only for the binary CPU language of PCs (x86/AMD64) and phone CPUs only understand a completely different language (ARM).
It is possible to get PC-style applications (command-line only, nothing with a desktop GUI last I checked) to run on W10M, but you need to completely jailbreak/root/"full unlock" the phone first. This is possible for most W10M devices but the process of doing so is out of scope for this question, and varies a little depending on the device. It also doesn't get around the binary language problem, so it's only useful for the small number of Windows PC EXEs released for ARM, or if you have the source code and know how to compile software yourself.
You must convert the installed and desired application (EXE) to Appx and change the architecture and OS in Appx to make compatibility with the device. When you do so, just sign the app and send it to Windows 10 Mobile and simply install and use it. This is one way and also risky because of the screen size and some options in the desired program. If you use this method or any other to start a desktop app, you're doing it at your own risk.