Reisen's right hand is often depicted to be making a gun shape, which leads to fan assumption that she shoots danmaku in this manner, and she indeed does in SWR. Some fans even depict Reisen holding an actual handgun in artwork. Those are all based on ZUN's word that her normal shots were modeled after a bullet. The revelation in SSiB that all Moon Defense Corps Rabbits are drilled with rifles suggests that Reisen can also use the real thing.
"Inaba" is a nickname given to her by Kaguya (just like Tewi). Her real name, Reisen, is written in katakana, but in order to fit in with people on Earth, the kanji with the same pronunciation, 鈴仙, was used. The characters for Reisen literally mean something like "Bell wizard", and Udongein "House of plantain flowers.". Additionally, in Japanese "reisen" can mean "Cold War". This may implies the time that human exploration of the Moon started. (see also notes on Reisen's spellcards) while in Germany it means "travels" or "voyages" as well as "to travel". Another meaning for "rei-sen" is "Type-0", as in the Japanese Navy designation for the famous Mitsubishi A6M Zero fighter plane. This may be also a reference to Reisen's military background. (see also Imperishable Night: Music) A species of rabbit, called the Deutsche Riesen, may also be where her name comes from.
"Udonge", the short version of the nickname Eirin calls her by, translates to "plantain flower," whose buds look remotely like rabbit ears. And it is also a Japanese Translation of Udumbara, and the symbol of Buddha's enlightenment and his reincarnation.
"Udongein",優曇華院 can be literally translated as House of plantain flowers, note that the character "院" (House) using in such circumstance is a vital part of Japanese Title system. In feudal Japanese society noble women would receive similar titles ended with "院" at their old age to indicate their worship to Buddhism. This title is similar to the Posthumous Name, 諡号 in order to commemorate a deceased person. In Reisen's case, "Udongein" was given by her master Eirin and this might probably a ritual practice to make Reisen forget her dark past and begin a new life on earth.
Reisen's Imperishable Night outfit, with a long-sleeved dark suit jacket, tie and short skirt, is considerably more modern than most of the other characters' and resembles a private school uniform. In Phantasmagoria of Flower View, with her jacket doffed, she looks more like an office intern.
In one of Reisen's images in SWR, she's shown wearing a necklace identical to Tewi's one (The necklace with a carrot hanging), but in no other picture shows the necklace. Maybe a reference?.
It's actually a tie tack, but it does look like Tewi's necklace.
Reisen's rabbit ears, strangely, always have two accoutrement-like buttons on them. It looks like the ears were linked to Reisen's head by buttons. Many fans made fun of this and said Reisen's rabbit ears were artificial. However, Silent Sinner in Blue chapter 8 showed other rabbits in the Lunar Defense Corps for the first time, and they also have the same buttons on straight ears, unlike the floppy ears of "civilian" Earth and Moon rabbits.
Reisen's stage theme in Imperishable Night is exactly the same name of a childrens' game, Kagome Kagome. Some of her own spell cards even support that name although the theme isn't included in the boss battle.