It's learned that Cortana has the best intel having spent the last years reassembling/assessing all the data and subroutines she has had.
It's found out that a dimensional seal "loop" gate has the original Gravemind trapped below the discovered ruins below Sword Base on Reach. The ancient Gravemind has been prodding war wherever able. It's learned this was even in the top of the Covenant as the prior top Prophets worked covertly for the being. The effects still rattle the remaining Covenant.
The Arbiter is tasked to find the remaining "Flood loyal" Covenant and works with Chief, Cortana, and the Didact directly. The Librarian is working with one of Cortana's "copies' on the recomposition made to life.
The only way to prevent war is to eliminate the Flood and provide the new composition to all life. The Didact amidst these revelations is on the brink of war siding the Covenant against Humans. Only a few Sangheili, the Prophets and Brutes stand against them. The Arbiter provides an uneasy truce.
The small bobble heads turn into "gathered protein synthesis packs". They can combine humans to transform the "host" into a new composed human with advanced intelligence, reactions, strength, and increased longevity. They are later noted to be immortal.
Chief and Cortana side with the Didact and reveal that the original Gravemind composed all life possible to die to provide hosts for the Flood. The original Gravemind survives and attempts to replicate itself as future Graveminds to protect against the Didact's return.
Due to the link to Guilty Spark and the experiments disrupted by Covenant presence in Combat Evolved, the Librarian is slightly less reliable and must be healed by Chief and Cortana due to programmed entity with the Didact who reveres Flood morphing.
When you shoot flood they transform themselves/host into a random composed human form. Composing the Flood is next. The Librarian has the resources and tools to compose the Composer into herself.
You tour the Covenant's homeworld eliminating rebels and Flood and encounter the new flood form. It's learned Forerunners in H4 are composed with cybernetic addition to resist the Gravemind. This explains Cortana resisting in H2-3
The Didact himself is learned to be composed into a being somewhat similar to the Gravemind and "why" questions are asked.