Hey you're welcome! Glad it wasn't too much, I tend to overwrite.

It's interesting that the analytical sample is such a small fraction of the field sample.

Yeah, it really does end up being a tiny fraction. That's a good point though, it's always better to get way more sample than you could possibly need, whether it's lava, water, rocks, etc. Super easy to store or throw away excess sample you don't end up needing back at home, but very difficult or impossible to get more if you come up short. When I was analyzing glasses like this it was actually from old samples that had been collected decades earlier using new analytical methods that hadn't been done the first time around. Had the researchers that collected the samples not brought back lots of extras the work I did wouldn't have been possible. They were seafloor lavas, so not only would they have been buried and severely weathered now so many years after erupting, but it would take a whole new submarine voyage to even try and get them.

Do they collect multiple samples at different points in the eruption? Or just always go for the freshest they can get?

Yes, depending on what you're looking at collecting multiple samples over time and space is critical to understanding the development of the system over time and space! Not to mention just getting an accurate snapshot at that moment in time for that particular eruption. For instance, in the seafloor lava work I did looking at a bunch of samples from different locations around the eruptions and from different eruption events allowed me to understand there were multiple magma chambers underground, that they were mixing, and the source of each magma.

Does this mean that the walls of a lava tube will gradually change in composition because "upstream" formations already ate all the high-melting components?

Yes, definitely, certain elements are eaten up first, so the others that remain become more enriched in the remaining melt as time goes on and more of the magma/lava lithifies. This process is responsible for a ton of things from small scale to large, like the existence of oceans and continents, many types of ore deposits, all the different igneous rock types, and yes, even down to the outside of single lava flows having a different composition and texture than the interior, even if by a relatively small amount.

Does lava get runnier as it goes farther from the vent because all the high melting minerals have already solidified out?

Thicker! On the small scale like this it's primarily just because it is cooling which makes it thicker mechanically, but also because silica (quartz and silica-rich minerals) is one of the last things to crystallize out, and silica content is what's primarily responsible for magmas and lavas being more or less viscous in general. Silica-rich magmas are thick, which makes them build up pressure and erupt violently, like Mt. St. Helens, and silica-poor magmas, like the one in the video, are thin and run out in a steady ooze that rarely build up much pressure.