Can a cable be used to transfer data from my iPhone 7 Plus to iPhone 16 Plus?

1. It needs to be a high-quality cable capable of carrying data, not just charging (if someone at Verizon said a charge-only cable would work, that person was an idiot). Whether there are any charge-only Lightning-to-USB-C cables I don't know, but you'll want to verify that what you have is certified for data. I would recommend getting a cable from a reliable brand - Apple themselves, Belkin, Anker, etc - not some off brand from some unknown Chinese company (not meaning to dis Chinese companies but many of these off brands come from iffy companies there).
2. I haven't done it myself, but lots of people have and reported success. I did my transfer wirelessly.
3. I haven't seen any reports of the time it took. Over the air my iPhone 12 -to-iPhone 16 transfer took about 15 minutes, if memory serves, not including the time it took to download all the apps.
4. I don't think so. But make sure you have a good backup if your older iPhone just in case things do go wrong.

Regards.

No, that will not work. However, you can use Quick Start, described in this link→Transfer data from your previous iOS or iPadOS device to your new iPhone or iPad - Apple Support. It will still need to download apps.

You can also use public Wi-Fi: Your local library, MacDonalds, Starbucks an Apple store, the Wi-Fi at any mall, many cafés, diners and coffee shops, even your doctor’s office in many cases.

But why is your Wi-Fi only 6mbps? Any router made in the last 10 years at least can go up to 600mbps. And an iPhone 16 with a 5Guc cellular connection can easily do 250 mbps, and even if you don’t have 5Guc millimeter service from your cellular provider available straight 5G UHF it can probably do 50-100mbps.