The latinum bars are soaked in fop’yano poison (first mention). Latinum, a Ferengi currency, is a metallic liquid which is encased in gold (considered by Ferengi to be worthless), and persists as a currency in the 32nd Century (last seen in DIS: “All In”).
Deuterium manifolds were mentioned in dialogue in VOY: “Course: Oblivion” and VOY: “Renaissance Man”, with deuterium being the fuel used in fusion reactors on Federation starships. A manifold distributes fluids and gas from one pipe to many and vice versa. In internal combustion engines, an intake manifold distributes the fuel-air mixture to the cylinders and an exhaust manifold distributes exhaust from multiple sources to a single pipe for venting.
Polarons are particles that can be used in weaponry (DS9: “The Jem’Hadar”) or for scanning for vessels (VOY: “State of Flux”), among other things. Polaron radiation is fatal to humanoids (DS9: “Apocalypse Rising”).
The Red Angel is indeed Michael, forming a major part of the plot for DIS Season 2. Michael and Rayner appear to have been transported to the end of Season 2, when Michael pulled Discovery along with her to the 32nd Century (between DIS: “Such Sweet Sorrow, Part 2” and “Far From Home”).
Michael identifies the second jump as being in drydock in San Francisco when Discovery was first being built. The original dedication plaque for the NCC-1701 says “San Francisco, Calif.”, so that tracks. The dedication plaques for the Shenzhou and the Franklin also were launched from the San Francisco Fleet Yards. That being said, the assumption was always that the fleet yards were in orbit, the scene in ST 2009 showing the Enterprise being constructed on Earth notwithstanding.
The next jump is to Stardate 1051.8, the climax of Season 2 of DIS (“Such Sweet Sorrow, Part 2”), the Battle near Xahea with Control, just before the time of the first jump.
Rayner identifies the culprit: a Krenim chronophage or a “time bug”, left over from the Temporal War. The Krenim were a Delta Quadrant species with the technology to manipulate time (VOY: “Year of Hell”). A chronophage is literally a “time eater”. The Temporal Cold War was a feature of ENT’s stories, which became a hot war around the time of the 31st Century (ENT: “Storm Front”), although the nature of a time war means that it was fought across different time periods. Eventually, as a result of the War, time travel was outlawed.
Stamets’ consciousness exists outside of the normal flow of time (DIS: “Magic to Make the Sanest Man Go Mad”) because of his tardigrade DNA, which he spliced into himself so he can function as the navigator required to use the Spore Drive (DIS: “Choose Your Pain”).
The fourth jump takes them to Osyraa’s hijack of Discovery in Season 3 (DIS: “Su’Kal”). The Black Alert was Tilly trying to jump away, but Stamets was interrupted before the jump could executed by an Emerald Chain boarding party. Reno is dressed in Discovery’s 23rd Century uniforms, since this is before the crew changed to 24th Century uniforms at the end of Season 3.
A Vesper martini is a cocktail invented by Ivar Bryce, a friend of writer Ian Fleming’s, who used it in Casino Royale, the first James Bond novel. It consists of gin, vodka and lillet.
The fifth jump takes them to 3218, 27 years in the future. Zora says that Michael and the crew died “decades ago” when the Progenitor tech fell into the wrong hands.
The Breen (DS9: “Strange Bedfellows”) are an antagonistic alien race usually hidden behind their masked suits. They were originally referred to as a Confederacy but in the 32nd Century are an Imperium. They have been mentioned previously as being in a state of infighting.
Michael refers to the first time she boarded Discovery while still serving her sentence for the mutiny she attempted on the Shenzhou in DIS: “The Vulcan Hello” that (debatably) set off the Klingon War.
The diagram that Zora flashes up is a light cone, used in physics as a way to visualize a path through spacetime, converging on the event where the past and future cones meet.
Chronitons are Trek particles with temporal properties and associated with time travel. World lines are curves in spacetime describing the path an object takes through spacetime, and therefore its corresponding history. Scravelli’s Constant is not a real thing as far as I can tell. Mark Rothko was an abstract painter known for his color field paintings.
Just as a note - the reason why Michael and Rayner are in their 24th Century uniforms and Stamets is not is because the first two are physically jumping through time thanks to being in mid-transport when the jumps started. Stamets remembers only because his consciousness is the one that retains its memory despite the time jumps, as he did in “Magic to Make the Sanest Man Turn Mad”.
Book pronounces raktajino in its usual form, so Reno’s pronunciation of previously must be idiosyncratic in nature.
The warp bubble does indeed insulate whatever’s within from the effects of Special Relativity - it has to, or else faster than light travel would be impossible. This is true whether or not you subscribe to the Alcubierre model for the warp drive (which I do not), the TNG Tech Manual version where the warp bubble lowers inertial mass (which I do), or some other method.
Rayner expresses concern that breaking the warp bubble would rip Discovery (and them) apart and Stamets says inertial dampeners will take care of that - which to me discounts Alcubierre once again because there are no inertial forces acting on the ship in such a model.
Airiam was Discovery’s cyborg spore drive ops officer who was taken over by Control and had to be killed (DIS: “Project Daedelus”).
Michael (and Michael) is presumably using Suus Mahna in the fight, a Vulcan martial art that T’Pol was also proficient in (ENT: “Marauders”). She finishes herself off with a Vulcan nerve pinch. Non-Vulcans have been known to use the nerve pinch, and Michael herself used it in “The Vulcan Hello” to disable Georgiou.