Right, so, if you don't know and didn't bother Googling it for yourself: Rosh HaShanah marks the new year of the Hebrew calendar. As Henrik says, it's said to be the day when God seals the names of the wholly righteous in the Book of Life, and the wholly wicked in the Book of Death.
Everyone else gets 10 days - the Yamim Noraim, or Days of Awe (Henrik uses both terms in this fic, as you might notice: the Hebrew term in his internal monologue, and the English one when talking to John) - to repent for their wrongdoings and ask forgiveness for them (to the person they've harmed, and getting forgiveness from God isn't the same thing, part of why Henrik is so distressed by the thought that so many of the people he wants to apologise to are dead). The Books are then sealed entirely on Yom Kippur.
Obviously, the Hebrew calendar works differently to the Gregorian one, so Jewish holidays fall on a different Gregorian date every year. In 2018, Yom Kippur fell on the 18th/19th of September. ...The 18th of September, 2018, also happens to be the day Roxanna died, according to the Order of Service for her funeral that we see in the episode The Three Musketeers. Yeah. Sucks to be Henrik, I guess.
On some phrases John uses (which he picked up from Henrik): "May their memory be a blessing" is the English version of a Hebrew saying used when someone dies. "G'mar chatimah tovah" is a High Holy Days greeting, meaning something like "may you be sealed for a good year in the Book of Life".
On that note, "tzom kal", which Jac says in her text to Henrik, means "easy fast".
Days in the Hebrew calendar start at sundown. Again, Henrik references this, and it's why he refers to Rox as having died on the day before Yom Kippur.
I was gonna have Sacha at the Kol Nidrei service, but then I saw that by the end of Inscrutable it's nighttime and Sacha is STILL at work. On Yom Kippur. Nice job, Holby. /s They could've set that episode ANY OTHER DAY, but no, let's just have the Jewish guy working through one of his culture's holiest days instead.
But there's also a Jewish rule - pikuach nefesh - about saving a life being more important than any other commandment, and it's why doctors are allowed to work on Shabbat/the Sabbath, so while I don't actually know for sure if it would apply to Sacha working past sundown on Yom Kippur let's say his reasoning was something like that anyway.
...Look. Holby created this mess. I'm just trying to clean it up. Like, idk, I could definitely see Sacha putting his patients above all else, but they could've just avoided the whole "Jewish character working on Yom Kippur" issue in the first place and set the episode on a different day so we didn't need to make up excuses for why Sacha was still at work? *shrugs*
A kippah is also called a yarmulke or skullcap. They're those little round hats you've probably seen Jewish characters wear in media before. Many Jewish men, and some women, also wear a tallit (or prayer shawl) on Yom Kippur, but in a lot of Ashkenazi (which I assume Henrik is) traditions they're only for married men and Henrik's never been married so I left that out to be on the safe side.
A yahrzeit candle is, as the description implies, a special candle traditionally lit to honour the dead. Yahrzeit candles are generally burned for 24 hours (so you can imagine why a lot of people use electric ones nowadays...), and usually lit on the Hebrew calendar anniversary of someone's death and certain holidays, one of which is Yom Kippur. They're most commonly used to honour parents, siblings, spouses or children. (Bolded the ones that apply to why Henrik would be lighting one.) But they can be used to honour others too, which is why Henrik thinks about the friends he's lost while lighting the candle.
Also re: candles, obligatory disclaimer that you probably shouldn't try the "leaving candles unattended" thing at home. Henrik and John just have no regard for their own safety.
Finally, a couple of notes on the story itself:
I'm afraid I don't remember who I saw come up with the idea that that pill we see Henrik take at the beginning of Inscrutable was a sedative first, but I used it here because it made writing sad tired Henrik easier and sad tired Henrik being looked after by John is cute (well, perhaps less cute in this context). Sorry for stealing your idea, whoever it was. You can have it back now I've used it, lol.
Yes, the scene in Henrik's bedroom was meant to essentially be an inverse take on the "can you bring her back?" conversation in The Three Musketeers. Yes, I've paralleled that scene in my fics at least three times now. I just love it a lot.
In canon, we never find out what Elisabet's brother's name was, only that he's dead. But I like the headcanon that Elisabet named Henrik after him.
I know Henrik probably seems OOC in this fic, but it makes sense to me that he'd be in a fragile, tearful state after just having experienced such a major loss. It's sort of meant to show how the repeated traumas he's been through over the years have ground him down.