Yay!
Now I'm just hoping against hope to see some cameos from the games relevant to how the series ended... I know they want to focus on the show's characters, and they should, but it would be cool to see some more familiar faces...
I don't think they have officially greenlit it, they just leaked that the show had been talking to California's government about a big tax break if they moved Season 2 there.
However, it's been Amazon's #1 show for a week and it picked up serious buzz and positive reviews. I suspect Season 2 will be greenlit, especially as the tax break basically means they get two episodes for free.
Yeah, I didn't check it myself but they've clearly set up for another season and given how well it's doing I will be shocked if they don't make another season.
As for your last point:
I didn't immediately pick up on House while watching (I was focused on something else when the scene played) but saw discussions of it since that confirmed it. Yep, definitely House, and the other guy he's talking to in the scene is Sinclair, the guy who built the Sierra Madre (setting of New Vegas's Dead Money DLC) and, in that scene, business representative for Big MT (setting of Old World Blues). The woman who is the Repconn rep I think is also referenced in New Vegas.
Given they should these New Vegas-related characters there, and we see Kyle going to New Vegas at the end of the show, I am assuming that Kyle is looking for House or something of Mr. House's.
A lot of fans seem to be assuming New Vegas as having been destroyed (I think a side effect of pausing and examining an image that was designed to be shown for a literal second) but that's not how I am taking the final shots. New Vegas looks pretty much as it does in the distance from the hills in the game, and the other shots suggest the aftermath of the battle for Hoover Dam. I would think if New Vegas had been attacked and destroyed, the Lucky 30 would have collapsed.
As an aside, I flew into Las Vegas airport on my way somewhere not long ago, it was cool seeing the Stratosphere from the airplane window. :) Oddly enough the Mojave... looks like the Mojave. I think some people shocked at how wastelandy the area around Vegas looked in that shot don't realize... uh, that's just the desert. That's what desert looks like.
A belated note, but there are a ton of little extras on the show's page that include both some great behind the scenes stuff as well as some Vault-Tec videos about how to be a good Vault-Tec employee.
Not to pick at old wounds, but the one about corporate alliances also shows Vault Boy and Pip-Boy together, showing they are not the same person. ;)
YouTube has some of the behind the scenes ones (this playlist has most of them plus some clips, etc.), but not the Vault Tec vids.