Nobody

城州住国重 – Kunishige living in Joshu The first two kanji must be 城州 (Joshu). 城州 (Joshu) is another name of 山城國 (Yamashiro province). The first kanji on the tang may not look like 城, but it must be a variation of 城 character. Ref. 「城」（U+57CE） | 日本古典籍くずし字データセット

應鈴木照雲師求源天秀鍛之 – Responding to the order from Rev. Suzuki Shoun, Minamoto Amahide forged this. I am unsure about 求.

The tag looks questionable to me. The town’s name Miyajima-cho (宮島町) was used after 1950. If the tag was written just after the end of WWII (1945), the town’s name should be Itsukushima-cho (厳島町). At the time, Hiroshima-ken was most likely written as 廣島縣. There are three 島 kanji on the tag. They are all wrong characters. 宮 looks strange. It looks like 官

関住兼松一則作 – Seki ju Kanematsu Kazunori saku (Kazunori’s family name is Kanematsu.)

入隊時の中隊長殿（十九年四月一日） - The company commander when he enlisted (1944, 4th month, 1st day). 陸軍中尉　堀米昇殿 – Army lieutenant, Mr. Horigome Noboru

藤次郎作 – Tojiro made 白紙 – Shirogami Tojiro is a trademark of the following kitchen knife manufacturer. TOJIRO Japan I More than just sharpness Shirogami is a brand name of carbon steel made by Proterial, Ltd.

於津國生玉剣竜子貞晴造之 – At Tsu no kuni (= Settsu province) Ikutama, Kenryushi Sadaharu made this. 慶應四歳辰八月日 – Keio 4th year Tatsu (1868), 8th month

The chiseled characters on the tang are imperfect because of wear and tear. But I think that the second kanji looks like 継 (tsugu). The name may be 義継 – Yoshitsugu. FYI: yoshtsug.jpg (91×250)

It must be a typo. 純正眞鐵入鍛 I do not know its correct reading either. Junsei magane nyutan (?) - Forged from genuin iron.

Just a guess, 蓋好資料之一也 (Kedashi ko-shiryo no hitotsu nari) – Probably, it is one of good examples. 金象嵌 銘曰 ＊ kin-zogan mei iwaku

小林 - Kobayashi (family name)

I think that your reading is correct. The nuance of "... saku ka" is conjecture rather than doubt.

大谷家之紋透鐔 (Ohtani-ke no mon sukashi tsuba) – Sukashi tsuba of Ohtani family’s mon IMO, the hanging wisteria crest on the tsuba looks a little different from the Ohtani’s Sgari Fuji.

東神正国作 – Toshin Masakuni saku 昭和十九年三月日 – Showa 19th year (1944), 3rd month

蓋同銘中無出其右者 (Kedashi domeichu sono migini derumono nashi.) – Perhaps, among the works with the same mei, it is second to none. As for “盡忠則命” on the box, I think that we do not have to be too bound by the word on the box. I guess that the order of the kanji was Kanzan’s own understanding only because he did not know the original four-character idiom 忠則盡命. The attached article was written on the premise that the word was 忠則盡命. Ref. 忠則藎命図鐔　銘　三信家