Yeah, yeast are incredibly hearty. Think about the activity you get dumping wort onto part of a yeast cake after the first primary. While I think a 2 week starter may be bad planning, it's perfectly fine to do.
Unfortunately the size and compaction of different strains varies so widely, volume of slurry is vague at best. As well as final cell count in a starter, they each like to propagate to slightly different densities. Slurry from cake off of a beer is even worse with hops and break material mixed...
That amount of time in a starter is fine. Up to 2 weeks is fine, after that I would think about giving it another wake up if it's a heavy beer. Pitch it.
Awesome. Saw that image and said, wow that looks familiar. Even so many years after the picture was taken and 15 years since I had been there.
Here is mine, kind of obscure, but a cool place.
20g is a ton, and outdated. Doesn't hurt anything, but is a huge waste, and can be hard to separate if the lacto is allowed to settle before pitching. You can avoid adding it at all if you keep the starter around 1.010. Lacto doesn't need much in the way of sugar to propagate, and pH drop is for...
They look good, but they're not super sturdy. I have some as work tables, they bounce around quite a bit. I use a wire shelving unit for a brew stand, cheaper and stronger, lots of places to mount pumps, etc.
I just made a lime Gose, start with 3 lime peels (no white pith) and 1 lemon peel (for 5 gal), soak in 100ml of vodka for 2 days, strain and add to taste at kegging/bottling. It's tasty.
I would worry more about wild or brewing yeast getting in during that time. Buchneri can take several days to sour anyway, so focus on making sure it stays sanitary. And yeah, chilling will slow down any further souring pretty well.
It takes longer than you would think to degas the CO2 in the keg, and its so low in a nitro beer, it's hard to really detect a small difference. I think I purge and recarb about every 1.5gal or so. Have to keep the N2 charged up as you pour, but it's pretty hands off.