Why is my disk at 99% usage here?

I've just seen your problem has gone away but below should be helpful for next time.

I downloaded your Process Monitor log and did a count for the number of times each file was being accessed during that 6 second trace you captured. You should be able to see this yourself in Process Monitor by going to Tools -> Count Values Occurences -> Select Path from the Column drop-down and then click on the Count button. Click the Count button to sort the count numbers in ascending/descending order. Double-click on any of those file paths to focus on them.

The top 4 file paths accessed are: 3276 times: HKCU\Software\Classes\Local Settings\MuiCache\de\417C44EB 3276 times: HKLM\SYSTEM\CurrentControlSet\Control\MUI\StringCacheSettings 2188 times: HKCU 1457 times: C: (this is the searchindexer that's accessing this)

Processes involved in the above accesses include SearchIndexer.exe and services.exe and they seems to repeating the request for accesses over and over again. Not I sure I know what's going on further than that but I suggest you try disabling your Windows Search indexer and see how that affects performance.

I also had another look at the trace in an unfiltered format and saw lots of access to various Software Distribution folders with paths prefixed with C:\Windows\SoftwareDistribution\Download..... so worth checking/disabling this and see how that affect performance.

  1. Does the disk usage really go up when free space declines? If so, why?

Yes. In Windows as well as other OSs a full main disk will result in OS behaving slowly/badly in my experience. Why? Fragmentation on disk (and the resulting increase of processing fragments in memory as well as number of disk read/writes). The remaining small area will be fragmented on disk, probably spread over different areas on disk. There is no spare space so de-fragmentation will not be able to help much until more space is freed up. All processes need to write temporary files (e.g. internet browser cache). These files will be fragmented. For magnetic disks the disk heads have to travel further which means slower file read/writes. For SSD disks I was not sure, this is a little bit boring but explains it well:
http://www.youtube.com/watch?v=VfYkJoqfG-k "Why Fragmentation is Still a Problem with SSDs".

In memory (in file-allocation-table in memory) fragmented files take up more space and result in more cpu and bus activity dealing with different fragments. On the video he ends up with a sell for diskkeeper which claims to improve the problem for SSDs. BUT allowing enough spare space on disk would probably be the best strategy.

This is good: Investigation into effect of de-fragging SSDs. http://www.pcworld.com/article/2047513/fragging-wonderful-the-truth-about-defragging-your-ssd.html

Conclusion: There is no point in running a de-frag tool with SSD.

  1. Can anyone deduct from my Procmon log file what program or process causes 99% disk usage?

I think you need to make some space on disk first. Get system to behave a little better. Then if there is still a problem look at disk usage (space or activity).