~ When Nyssa landed on Terminus, she had to rely on really ancient and inadequate translation software for a month or so until she learned the local language. The bad translations actually helped her integrate with the group, because she was much less of a stick in the mud and much more entertaining. However, she and the Garm got along perfectly well with hand signs.
~ Most of Tegan’s stuff went into storage after she was dropped off, but Nyssa kept Tegan’s Black Orchid dress on the stand by her bed. Good memories. (This is actually canon; take a look at Nyssa’s room in Arc of Infinity.)
~ The Doctor set her to work doing maintenance on instruments and equipment in the TARDIS lab in an attempt to keep her from nagging him about TARDIS repairs. It didn’t entirely keep her out of his hair, but at least his lab was in better working order by the time she left.
~ Tegan tried to teach Nyssa to swear but finally had to give up, because the TARDIS translation circuit’s obscenity filter turned nearly everything into “rabbits.”
~ Nyssa is one of the few companions who likes all the Doctor’s cooking. Or, rather, the food machine’s.
~ Nyssa learned English while staying in Stockbridge. (She definitely knew it by the time of Fanfare for the Common Men.)
~Her interocitor invention is one of the Doctor’s prized gadgets, but he doesn’t use it much because he was so upset by her departure that he put all her things away somewhere deep in the TARDIS and then couldn’t bear to go through them for any instruments or tools he needed.
~Nyssa’s, Tegan’s, and Adric’s rooms all appear to be on the right side of the first corridor going in (although Adric’s is some distance away from the others, possibly in the next hall down); I think the Doctor’s room is on the left along with the kitchenette with the food machine seen in early Who.
~Some of Nyssa’s lovely china and glassware on that curio cabinet in her room is a tea service gifted her by Queen Victoria in Empire of Death.
~Nyssa would go and work in the Cloisters, pruning and tidying, when she needed to settle her nerves. They reminded her of home.
~They were also a good place to dance. She told Tegan in Black Orchid that she was “quite good, if I do say so myself,” which is the nearest we ever get to a boast from Nyssa, so apparently she really enjoyed dancing.
After their work with the Lazars wound down with the invention of a cure in the early 3500s and a vaccine around 3512, the elderly Garm began to fail quickly. He’d lost his purpose in life. However, when Neeka was born, he suddenly had a baby to dote on. Unfortunately, Nyssa and Lasarti moved to Zarat, Lasarti’s homeworld, within a year of the baby’s birth — they seem to be living off-campus from a hospital in Circular Time — and the Garm deteriorated quickly after they were gone. Nyssa had been the only person to treat the Garm as a colleague rather than an intelligent animal (Lasarti didn’t do that, but he had been terrified of the Garm when he started dating her, convinced her bodyguard was going to decapitate him, and he never entirely got over his fear.)
~Nyssa is one of the very few companions besides Romana that the Doctor will let fly the TARDIS, although only in an emergency; he seems to have taught her a great deal during the S19-S20 audio adventures. There’s a story in 1001 Nights in which he tells her, “the carpet is yours to fly now,” which she then does to save him, paralleling her flying the TARDIS back to him at the end of the audio. Turlough tells the Sontarans that Nyssa’s the only one of them who knows how to fly the TARDIS (of course, he could be lying). And there are various times when the Doctor’s having her check readings or operate some of the controls when he seems to expect her to know how, including the most recent audio, when she does something clever, complicated, and FAST to keep the exterior shell together when the whole TARDIS is in imminent danger of falling to pieces.