Can I stop my modem from gathering and sharing our data?

There is no data stored in the modem. Activity tracking is via data stored directly in the browsers on the individual devices. More likely there are apps and/or log-ins to sites or services that are visited in common among the devices.

Modems are like a bridge over a canyon. It's a pathway with traffic in both directions. Nothing happens to the signals travelling through it.

In what you're describing, the browser is complicit. You're describing use tracking leading to what are intended to be user-relevant ad placements using cookies and activity history in your browser. It's a good practice to set the browser to erase everything when closing. Alternatively, you can do it manually.

No, not a browser/software issue since my husband ONLY uses his phone and does not log in or use a browser either on my phone or on my computer. He never uses either device. The ONLY thing these devices share is the Wi Fi Internet connection. And I don't visit LazyBoy recliner web sites either, on my phone. Never. We don't even share social media, I'm not connected to him even on FB and that's the only social media I use. Not even connected via Google sharing sites.

When accessing an internet website from a phone, if a bespoke app isn't being used, the connection is made using a browser.

Many browsers will sync multiple instances on different hardware for the same user. History, bookmarks, preferences, etc., are all shared and synced. If the phone browser in use is either Firefox or Safari, for example, the browser history would be exchanged when that user goes to Firefox or Safari on other hardware.

I don't use Safari. Firefox can probably share history, bookmarks, etc. between devices if the user configures the Sync feature and logs-in accordingly on multiple devices. I don't. I use Firefox on three computers and one iPhone all on the same modem and router. Nothing is synchronized or shared from one to the other ... except perhaps if I access/log-in to YouTube (or other such site) via the same log-in for the particular site/service. I also access YouTube via a smart (Android OS) TV and have noticed that the suggested video feeds on it are sometimes reasonably different than on my primary computer. I have an adblocker in Firefox on the computer so I never see ads when perusing YouTube on it. Can't install an adblocker on the TV so the YouTube app on it has ads..

Please explain HOW a browser software program can access browser information from a device that is has zero connection to other than a wi fi signal, and transfer it to the browser of that device, even though that device has zero connection to any other software on any other devices. Including log ins. Because if that is true, then if you use your device and browser software in a coffee shop using their wi fi signal, does that mean that now your browser has incorporated all the cookies from all the same browser software of all other users? I would hope not . . .

I will also reiterate that these devices are not shared for use, they are used by one person only. The only common link is a common brand of browser software installed and wi fi connection. But not common log ins.

Also creepily, I was talking to my Dad yesterday on the phone (analog phone, not digital) and mentioned ordering printer ink from Staples and then I started seeing ads for Staples on my fb feed. My husband has this Echo device in the room where the TV and phone are, supposedly only activated by a prompt and not listening . . . I have repeatedly asked him to turn it off that I don't want it around but he refuses.

" Please explain HOW a browser software program can access browser information from a device that is has zero connection to other "

Look up browser syncing for more information. I'll reiterate that a device's connection has nothing to do with this topic.

Your question had to do with a suspicion that your modem played other than a passive role for data communication and I'll assure you that it doesn't. As for how and what an Echo does, I can't help you.

OK, if not modem, what? You said, "Browser synching" but you have to activate that feature of a browser, and if a user is not activating it on a device, it should not be able to synch with some random other device out there. Sure, I can synch my phone browser in Chrome/Google Apps to my laptop browser, because both store data in a cloud that I can access when I am logged in, but my husband's phone should not be involved. He's not using either of my devices, nor is he logged in on any device under my password, and I never use his phone.

Synch in Chrome

I've been assured before that an Echo device is not listening, but I've also experienced it butting into conversations without it being activated by it's wake word by any stretch of the imagination.

For some browsers, sync "on" is the default setting.

Again, how can a browser that is logged in to someone else's account, sync with my account which is also password protected and not logged into their account, without a person doing it? If that's the case, passwords and separate accounts would not mean anything.

A quick Google tells me it's possible for both Echo and your wi fi router to track and pass your data on to third parties, despite lengthy denials by their parent companies. Not sure that I could stop it though, other than my said desire to unplug the Echo device.

https://www.cnet.com/home/internet/yes-your-router-collects-data-on-you-heres-how-to-protect-your-privacy/

https://www.digitalstrike.com/does-alexa-spy-on-you-heres-how-voice-data-is-used-to-target-you-with-ads/

Wifi routers are pass-through devices like modems. They "do" nothing else.

Your home network's IP address is being targeted. Every device connected to it has the same IP address.

https://www.cbsnews.com/minnesota/news/targeted-ads-internet-mobile-devices-websites-shopping/

You can see your IP address at https://whatismyipaddress.com/. Try it using different devices connected to your network. They should all be the same.