Yes. There is an e-shop which let's you buy and download electronic copies of the games. Or you can buy a physical copy games.
You can also get You Tube on switch. Not sure about other stuff like Netflix etc.
I have an Oled and my kids have the older ones. The oled has a bigger and clearer screen. But this only applies when you're playing hand held. The picture quality is the same on the TV. The oled also let's you connect your switch to an ethernet cable (so wired Internet connection). Normal switch is WiFi only. I think the stand on the back is different as well.
As long as your TV can take an HDMI cable, it can run a switch.
It comes with a charger and docking station. If you want to charge it or play it on the telly, you put it in the dock.
I would always recommend buying the original model rather than the lite (hand held only) model. Even if you rarely play it on the telly it is less faff finding chargers etc with kids when it needs charged. And you can play it on the telly while it charges. It also lets you play games multi player as you have two controllers.
If DC want to play games with their friends online, they will need to subscribe to Nintendo online. There are various opinions, single or family (if you have more than one switch). There is also an expansion option that is more expensive but gives you certain online games and download able content for games. IIRC, it's about £50 a year for the family expansion online subscription.
Make sure you password protect the e-shop and also password protect your card details. You also don't need to save your card details and I'd recommend not saving them.
There is a parental control app but IME it doesn't actually block the switch, just has an alarm to tell them when time is up. It also allows you to see what they are playing and for how long etc. My advice is monitoring your DC rather than relying on a app to do it for you.