Regarding the date,
Please note that Im really beginner in Nihonto topic, so my opinion may not be worth anything..
I have a feeling that there is some part of date missing on Mei,
Knowing that Koka Era started at December 2, 1844 of Gregorian calendar,
could Mei say this, rather than 2nd month?
I may completly misunderstand the Kanji behind signature, if so then im sincerely sorry!
Also ive tried help of chat gpt regarding the date,
Here's what it says:
"Kōka 1 (弘化元年) runs from Dec 2, 1844 (Gregorian) — the date of era change — through to about mid-February 1845, which is when the next lunar year begins.
The 2nd lunar month of Kōka 1 then falls in late Feb to late Mar 1845.
Only after the lunar New Year (around Feb 1845) does it become Kōka 2."
"So as you can see, Kōka 1 doesn’t end with January or February—it continues through the intercalary month and into March.
Therefore, a date like 弘化元年二月日 (a day in the 2nd lunar month of Kōka 1) corresponds to sometime in March 1845 (Gregorian)."
Its a GPT only so it may be in complete wrong,
Best regards,
Daniel