RIP What are those thin rings around the thick rings?
The clearance that needs to be maintained by unrelated nets. You might note that the track for Net-(U2-Pad3) makes a tiny little jog around pad 7's ring.
RIP Should have been both tracks for pad 5 and 4 more to the right
The track to pad 5 (net E3), looks fine in that picture. The track to pad 4 has some wasted copper, where it looks like the track tried to go to the left and then you brought it back, but it won't have any negative consequences.
RIP Another thing that confused me is the warnings of silkscreen being "erased" by the copper tracks.
Are you sure it is referring to tracks, or to the copper of the pads? You've got silkscreen going over pads 8 and 7 in that picture, which, as it warns, will have to be omitted.
You're right that copper which isn't intended to be soldered to will be covered by solder mask, and is a legitimate place to put silkscreen. That just doesn't apply to all of your copper.
RIP I need to select the accuracy I want (sigh, can't they figure it out from the file I'm uploading???)
Perhaps you want even tighter tolerances than what appears in the file. How would they figure that out?
If you specified 8, they might catch it and warn you when they do a manual review. Not all of these checks boardhouses have are fit for generating automatic feedback to customers.
RIP I selected 6mil, which costs (marginally) more but more importantly prevents the use of the 2oz Cu density (which may be overkill, but it's almost free at 8mil accuracy)….
Absolutely no need for 2oz copper on the sensorboards. The only value is for carrying higher currents.
I'd pay for the service which matches the tolerances you used, the risk/reward/frustration tradeoff isn't great for trying to save those pennies.