Pretty sure this is Tithe: A Modern Faerie Tale (2002) by Holly Black, the first book in the Modern Faerie Tales Series.
Here's a summary which covers most of the main plot points.
As with Triss, Kaye Fierch is unaware of her status as a changeling at the beginning of the novel, although she is aware that she can see fairies. Kaye is a pixie and her true ...
A Redditor found the book (or books).
Seems I was either remembering pieces of Ann Pilling's Black Harvest from her Dark Powers series, or my memory was combining elements from different books from the series.
The Dark Powers books are still in print.
Another possibility that involves a young brother and sister, with mystical aspects rather than a time travel machine, is Astercote by Penelope Lively, first published in 1970. From the author's website:
Astercote village is dead, its ruins lie hidden in the murky wood. Mair and her brother, Peter, come upon the deserted village by accident and there meet a ...
Could it be Connie Willis's Doomsday Book? It was published in 1992, so the protagonists could have been from the 1980s. It's got young people (but the main characters aren't as young as 15-16), time travel, Black Death... but other aspects are different.
Young historian Kirvin gets sent back to 1320s Oxford, but there's a malfunction and she lands in 1348 ...
Fire & Flood by Victoria Scott
Tella Holloway is losing it. Her brother is sick, and when a dozen
doctors can't determine what's wrong, her parents decide to move to
the middle of nowhere for the fresh air. She's lost her friends, her
parents are driving her crazy, her brother is dying--and she's
helpless to change anything.
Until she receives ...
Sounds like the Star Shards Chronicles Series by Neal Shusterman. It's comprised of three novels, published from 1995-2002.
Scorpion Shards (1995)
Thief of Souls (1999)
Shattered Sky (2002)
According to the TV Tropes page, the trilogy centres on six high school students who gained powers as the result of a star that went nova at the same instant they were ...