Is there anymore information provided on the crystal's origin in the 2003 series, other animated series or comics?
When the first issue of TMNT really took off and Eastman & Laird were not only able to pay the uncle's $1300 gift back but able to start running 2nd and 3rd printings and keep the comic going, they took the time to use their soapbox to plump for Kirby's ongoing battle against Marvel for—at minimum—some of his original artwork.
Each issue of the first series of TMNT comics took months and was often months late (notably, No. 16 was printed before issue 15) but many people were just getting started: orders kept coming in for the first issues, which were reprinted and then entirely redone with better inking and lettering and then reprinted. They also did art and worked with statting out Palladium's TMNT RPGs.
In between the early issues, Eastman & Laird published one-off adventures that fit their new universe but not the narrative arc of the first ten or so comics. Because of their vocal support for Kirby, they included a petition form for readers to send to Marvel in one of their issues and devoted Donatello's 1986 one-shot to him, weaving a story about his drawings coming to life. He and his creations were statted out in Palladium's 1989 Transdimensional TMNT.
In Turtleland, Kirby was a tenant in the brownstone owned by Mr O'Neil. By the beginning of the series, April's dad had suffered a stroke; she'd been a hacker as a teen and, after finishing her Master's, got a day job helping Baxter Stockman program his Mousers. After losing her job helping the Turtles defeat Stockman's plan to bring down one of the World Trade Center buildings, she rented out an office space in her front cellar to Kirby to make ends meet.
is as much backstory as you get for the crystal in Donatello's comic or in the RPG. He first assumes Don is an alien coming to reclaim the "warp crystal", but that was just his reaction to seeing a talking humanoid terrapin and not necessarily its actual origin. He and Don later travel through a portal he had drawn to "Kirby World" where his creations—which he thought had been vanishing—thrived and oppressed the local people. Kirby defeats his own monsters through his art, saves Donatello (every early TMNT ends with someone else saving the day), and presumably becomes the resident sorcerer of his own universe while leaving ours. (Kirby was old and close to death at this point; he was trying to get his art from Marvel to provide for his family and deal with medical bills.)
Muuuch later, 2 years after the TV episode you're asking about, Vol. IV No. 22 came out, reprising the Donatello one-shot and the style of April's montage through Mirage's missed deadlines in Vol. I No. 11—No. 10 had been a Christmas story that got published in April so they used 11 to play catchup—to tell the story that April O'Neil herself had been created by Kirby's magic crystal. Her mom had become barren after her older sister's birth, and dad discovered the warp crystal in some estate junk he had purchased en bloc at a sale for his used-goods shop.
He eventually hit on using the crystal to deal with his wife's infertility and, after two miscarriages, April was the result. She and Renet—who've been watching this all as lusty time-traveling cockroaches—inexplicably steal dad's crystal and dump it into a floor vent before dying. Taking this at face value instead of as a commentary on Laird's own age and experience as an cartoon artist, Kirby had presumably found the crystal in the room he rented from April.