The APC Pro 1350VA would be overkill for such a relatively tiny load of one Wi-Fi Modem and one typical Router. As the model number implies this UPC can output 1350 Volt Amps. If your devices have a wattage listed, you can take the volts (probably 120) and see how many times your device's amps divide into that number. If you purchase one of APS's models in this line (they range from 1100 VA to 1500 VA), the included software run on a PC will tell you how long the UPS will output 120 volts when your Wi-Fi Modem and Router are actually plugged in and under load. It will probably be several hours. As an example the power consumption of my home theater is fairly high. It includes a 75” TV, an Xbox One X, a Denon AVR-S730H Receiver pushing a 5.2.2 Surround system, a Western Digital NAS and a 10” and a 15” Powered Woofer. When plugged in to the UPS and under load, the PC program tells me it can maintain that load from the battery for 45 minutes.

The flashing purple/blue LED on your earbuds is only telling you that the earbuds are ready and TRYING to pair (connect) with anything within range that can potentially pair with. Turn on the Bluetooth Pairing function of your phone and see if your phone can see/recognize your earbuds. Sometimes Bluetooth devices can only connect with each other if both of them are in the active seeking mod.

I THINK you're asking about the Noise Reduction feature. I have Bose Quiet Comfort 35 II Headphones and the Sony WH-CH700N Headphones. Using them while cutting grass or leaf blowing, I find that the Bose reduces a much wider frequency of sounds and gives you a cleaner version of the sound you want to hear (Podcast, Music, Etc.) at the same time. I found that when using the Sony I had to adjust the Podcast's volume much higher than I wanted to, to hear the Podcast voices over the lawnmower noise. It should be considered though that the Bose Quiet Comfort 35 is MUCH more expensive than the Sony WH-CH700N. You get what you pay for.

Like you, the "Smart TV" features were of no interest to me as I turned my Sony - 75" Class (74.5" Diag.) - LED - 2160p - Smart - 4K Ultra HD TV with High Dynamic Range on for the first time. That meant I had to plow through dozens of screens asking me to enter my google account (I don't have one) and other information to access the Smart features. After a few minutes of that I managed to get to the end of the set-up process and it hasn't asked me again since. I would recommend though that if you can, you should hook the TV up to the internet just once. That way you can receive the inevitable TV software operating system "Updates" that are sometime needed to make the TV operate properly. It's just the way it is nowadays. Because they expect "everyone" to have access to the internet, manufacturers are more willing to ship new products that really aren't fully tested or developed. As you know, it takes months for some of them to get from the factory to the home, so getting it on the water as fast as possible seems like a more important thing that perfecting the software. I also think they use the early adopters of models to do quality testing for them. If enough of us complain of some operating problem, they can make the change and send it to us over the internet later.

With a very fast internet connection, it still took about five minutes or so for my Sony 900E to update before fully operating for the first time. It was worth it though. It's a great TV.