Hi Jennifer,
Thanks for posting and welcome. I understand your frustration. I'm wondering what plan they recommended after you explained all of this to the agent. I would expect our top tier option. You currently are on our Prime plan. Which at the time wouldn't accommodate your household. Is that the original plan you signed up on? We have recently updated all plans to have "Plus" options, including smart browsing. This was reserved in the past for our higher tiered plans and is now standard. This upgrade is at no cost, but we should certainly have your call reviewed before we decide how to move forward. While you wait, let me just give you some more information that I hope answers some of your questions.
Gaming is possible on the system. Twitch based shooters will not work, however turn based games like MMORPG's work just fine. Streaming as well and most of the applications you listed. What I think was left out of the explanation is that a very good router would be needed to maximize the speed to all devices present in your household. For example if all 7 of you are online at the same time. A basic to medium level router would only be able to effectively provide enough bandwidth speed to around 3-5 devices. What each device is doing would affect this as well. The more computers, phones, and tablets connected, the thinner your bandwidth speed is spread. You currently receive 10 Mbps from "Prime", divide that up and it leaves you with a smaller amount for each connected device. Netflix, Pandora, and gaming require a minimum bandwidth speed to work. Unless you directly connected one device to the modem, or only had 2-3 devices you'd probably experience buffering/connection issues.
Finally the data allowance needed to not run is not sufficient under Prime. Although you can always purchase token bandwidth when needed. Sale call reviews can take a few days depending on how long ago it was, and the sales source. However once I have more info I will let you know. If you have anymore questions or concerns feel free to let me know.
Thank you,
Chris