Just log into your routers admin panel and see if there are any online devices online that arent yours? That would be my goto because then you can just block them from the panel?

otherwise via linux cli you can do arp-scan and youll see online devices in your subnet. Theres also a few options to scan different interfaces

Checking the router is probably the only way to see if someone is active on your network.

Can anybody hack your computer? No. Most people only know how to run scripts that are known and patched in most operating systems.

There are skilled people who may be able to create an exploit or find a vulnerability in your computer, but they will mostly target businesses or people they know will be worth it to hack, so most likely they won't bother you.

Generally if your on your own WiFi, having a WPA-2+ personal password is enough, but the more paranoid may have an IDS/IPS on their home network.

If your out and about, I'd personally use a VPN. I don't like public ones and like to recommend setting one up on your home WiFi instead.

If you think you've been hacked.. change your passwords and run virus scans. If you still don't feel safe, backup your data and reinstall your operating system.

I forward all router logs to a syslog server which then parses and alerts me of "unknown Mac addresses" joining the network as soon as even one log shows up. If you have a syslog server and some way to index/parse those logs, that's one way to do it

WiFi is really no less secure than wired aside from being harder to keep people from having physical access, and since most home users don't use any kind of connectivity protection on wired ports it might even be seen as more secure.

Couldn't you just monitor your WiFi at the router level?

Anyway you can use nmap to scan your entire network to find all connected devices. Its not foolproof but its a start

You can use arpwatch. It reports new mac addresses on a given network interface.

Here's my setup. I have a raspberry pi running pihole and unbound. I set that raspberry pi as my primary dns on my router. Now in order to use the internet all devices will make dns queries over wifi (you can use a wired pi as well) to the pi which means it will also see all devices using your wifi and notify you when a new one shows up or if an ip changes mac addresses.

Keep in mind these notifications use smtp (email) and you most likely need a mail server to receive them.

I have a matrix server on my network that has postmoogle (email bridge) that can receive the emails from arpwatch and send them to me as a matrix message