While it's not surprising to have Murakumo use a katana as his weapon, when one recalls that the original name of the Kusanagi no Tsurugi (one of the Three Japanese Imperial Regalias) is Ama-no-Murakumo-no-Tsurugi, it becomes quite a nice detail.
Why would Akatsuki's stage be located in the Aokigahara forest? One would think it's just for the closeness to Mount Fuji aka one of the most iconic places in Japan, or because the forest is the top one suicide spot in Japan so few would approach it, but Aokigahara has been associated with death for centuries... and specially with the ubasute practice that involved abandoning one's older relatives to starve there in times of famine. Since Akatsuki is a Fish out of Temporal Water who was "forgotten" for 50 years and then sought after when he resurfaced thanks to his links to the Blitz Engine, it makes an eerie sense for him to choose Aokigahara as his hiding place.
The deal above with Murakumo goes into Fridge Logic when one recalls that the Ama no Murakumo is traditionally represented as a two-handed sword and nota katana, like the one Murakumo uses. Rule of Cool, we guess...
forest? One would think it's just for the closeness to Mount Fuji aka one of the most iconic places in Japan, or because the forest is the top one suicide spot in Japan so few would approach it, but Aokigahara has been associated with death for centuries... and specially with the ubasute