Seems the driver of your Wireless Adapter is corrupt. This could be result of malware trying to replace it, or something like that.
I would first scan and clean the Laptop from any possible malware using the built-in "Windows Defender" and Malwarebytes Antimalware. I would make sure to uninstall any unnecessary/possibly malicious software.
Then, you can try uninstalling the wireless adapter driver from "Device Manager", and installing a fresh one after reboot.
To answer your other question, using a modem is no more secure than using a wired network. If your laptop is compromised and has some type of malware, the type of connection to the internet doesn't really matter.
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