To the Wheeler question, I would say he was just wrong. Pre-eminent physicist of the 20th century he may have been, smarter that I'll ever be, but he was also n

To the Wheeler question, I would say he was just wrong. Pre-eminent physicist of the 20th century he may have been, smarter that I'll ever be, but he was also nearly 90 at that point and had retired 22 years earlier. To (1), he's talking about the distance ladder. Distances to various galaxies were computed by the teams involved in developing the LCDM model by scouring the skies for instances of type IA supernovae in this galaxies. When these are called "standard candles," what that means is that the luminosity is known and thus the distance can be computed using the inverse square law by comparing the observed brightness to the known luminosity. Historically, this wasn't a super-reliable method and yielded some bounded error rate for various reasons, including dust causing some reddening of the light that could be mistaken for redshift, as well as the fact that type IA supernovae are not all collapsing stars of exactly equal mass and you might catch them at different times after the initial supernova. What Wheeler probably didn't realize at that point was the methods and frankly just downright tedious repeated measurement work over the course of decades that astronomers had been doing to make this more reliable and accurate. If you want to know all about this via first-hand account from one of the astronomers credited with the dark energy discovery, read The Extravagant Universe by Robert Kirschner. It's very accessible, not super-technical, but goes into painstaking detail on exactly how astronomers made the type IA work as a standard candle. It's also just a great testament to the work involved in experimental astronomy, down to the logistics of convincing a scheduling committee for the various telescopes capable of seeing that far that what you're looking for is worth looking for.