I've used that exact fast lagering method for about 15 brews. It certainly could not hurt to do a more traditional lager afterwards, but the whole idea is for that to replace a traditional lagering. Don't know if this is accurate, but the way I conceptualize it is that doing the end of...
I brew with the Grainfather in my basement, too. There's a humidifier in the room it's in (a laundry room, maybe 10x10), and I crack the small window that's in there during the boil. Doesn't seem to create any problems.
Also enjoyed beer from the beginning. When my college friends were getting cases of Busch Lite I'd be grabbing a 6 pack of Sam Adams (when many people had never even heard of it).
Got a 1-gallon all grain kit for Christmas from brother-in-law. That was brew #1. Doing #135 tomorrow.
That seems to be the perfect kit for what you want. And I'd definitely get the US-05 yeast option. One packet is plenty.
Let us know if you have any more questions, but even if you don't report back how this turned out!
Whirfloc will help clear the beer, regardless of whether you cold crash. Cold crashing is nice, but only speeds up what will happen anyway, so it's not something to go out of your way to do. Nor should the inability to do it preclude you from doing a pilsner.
Your bigger issue is that the...
Yep, sure do. Sometimes it's made with walnuts, but I don't like pesto enough to even bother asking anymore. Luckily they are expensive in the US so pretty easy to avoid. A little tougher in Europe.