Connect cell phone to laptop?

Must transfer a picture. Can you do that without a cable?

WhatsApp Web, assume that bluetooth is not working for whatever reason.

Of course, that's called a home network.

https://www.dasheimnetzwerk.de/einrichten/Einrichten_OS_Androidx/Kapitel_Androidx_Einrichten.html

Via Facebook or Mail or Insta or WhatsApp or cloud

There are a few options.

Here is a small selection:

Bluetooth
WLAN (e.g. Via a shared folder on the laptop)
Any cloud service
Memory card
USB OTG adapter and USB stick
Wireless ADB (at least with a rooted Android device)

If it's an Android device, first copy the image to your Google Drive.

Then install the following on the laptop: https://www.raidrive.com/ With this you can set up Google Drive as a drive letter. Then you can easily drag it from Google Drive to your laptop.

If it is an iPhone, first install the iCloud app on the iPhone. Then you install the iCloud client on the laptop: https://www.microsoft.com/...ktq5699m62 There you log in with your Apple account. Then you can copy the pictures over.

With both, you can do it the other way around.