DD13 (8th grade) took this in school. Can anyone comment on it? I'm having a hard time understanding how the scores translate to something I can wrap my head around.

dd14 (8th grade) took it as well. She scored 1124 total. I think that was 95th percentile

The CB has changed the scores for all of it's (P)SAT family of tests to be on the same scale. So PSAT 8/9 scores are supposed to approximate what the same student would have obtained on the SAT, if it were to be administered at that same time. This does also mean that the possible scores obtainable on the PSAT 8/9 are not exactly the same as the SAT, as both its max and min are lower (240-1440). So the scaled score compares students to college-bound seniors, though with a lower ceiling.

Then there are grade-based percentiles, which compare students to their grade-peers. E.g., the score f&esmom cited above is about the 97th %ile for 8th graders in Fall 2017, and the 92nd %ile for 9th graders in Fall 2017.

One hopes you both received this document with your DC's scores:
https://collegereadiness.collegeboard.org/pdf/psat-8-9-understanding-scores-fall.pdf

For kids at the upper extremes, the ceiling on the PSAT is too low. DS' score unavoidably dropped almost 100 points compared to his SAT score from 7th grade because the maximum is only 1440 compared to 1600 on the SAT.

Beyond this obvious hard ceiling issue, there is also a soft ceiling issue. You needed a perfect raw score (0 incorrect) to score 1440 on the October version my kids took and missing 1 math question dropped your score 20 points while 1 reading or 1 writing question dropped your score 10 points each. While DD's score did rise compared to her 7th grade SAT score, I am fairly confident that her PSAT score is an underestimation of what she would have scored on the SAT at this point in time. There is more room for imperfection on the SAT and a score as "low" as 1440 (PSAT max) on the SAT would correspond to many missed questions. In other words, at the upper range (say above 1350) of the PSAT, I wouldn't assume that is a correct estimate of your child's SAT score.

Another issue is that the national percentiles are meaningless and overinflated. The "user percentiles" are closer to reality and the one you should reference.

So if DD's score is 99+% for her grade, despite being well below the max, is it probably safe to think she'll do very well on the sat, or is this such a vague/blunt instrument that it's pointless to speculate?

If she is at 99+ user percentile on math and on EBRW, then she should do quite well on the SAT in three to four years as long as she maintains a normal growth trajectory. If she is far enough from the ceiling scores, then the PSAT 8/9 report's estimated future scores for PSAT/NMSQT can probably be trusted roughly.

I don't see the estimated future scores--am I missing that? I don't have a paper report. The scores appeared in the school portal and DD told me about them.

The paper report has a lot of details but it looks exactly like the one in aeh's link. The estimated future scores can be found when you select report details on the college board website. You can get a lot of additional details on the college board website, like user percentiles, score ranges, and answers/explanations for the questions. If your daughter has turned 13, then she can create a college board account and access her PSAT report in greater detail then the official printed Score Report. The estimated future scores do not provide any profound insights - as an example, it unhelpfully predicts that DS will score 710-760 on the math portion of PSAT 10 based solely on his 720 on the PSAT 8/9. Keep in mind that the SEM is +/- 30 points and there is a presumption that scores will rise on average from year to year.