We too, break the kata down into individual applications. The fighting forms, from what I understand, is the adaptation to an attack by multiple attackers, it could be in sequence or not, and the defending student, when attacked, is required to attempt the techniques, say from Pinan one, to the best of their abilities.
From everything I have read, forms were NOT designed against multiple attackers. While this was a popular conception in the latter half of the 20th century, modern understanding of kata has it that each short series of moves is a way of handling individual attacks. These were then combined and lumped together as a kata for a convenient way to remember and practice the moves.
Think about a collection of short poems by a particular writer. Each poem is a stand-alone work but collected and published into a single book. The individual poems are not necessarily related to each other, though may share qualities of the writer's style. I think this is a good analogy for kata.
To address your other question: Isshinryu kata curriculum includes in order: Seisan, Seiunchin, Nahanchi, Wansu, Chinto, Kusanku, Sanchin and Sunsu. All, except the last are often common to other Okinawan styles, albeit with some differences, and even Shotokan under different names. Weapons include generally Kusanku and Chatanyara sai (some may still teach Kyan no sai), Tokomine and Urashi and Shishi bo, and one tonfa kata called Hamahiga.
