Here we go...
I am doing this analysis from when he opens up the Cryo Capsule to the end of the video.
First, I believe a "Reasonable Explanation" for his armor changes is the Positive/negative pressure that The Chief underwent in space.
Cortana looks different. Did she do something with her hair? (No seriously, AI's can change their appearance.)
The Pistol MC picks up looks to be either some entirely new weapon, or a heavily modded pistol. Clearly has an RPG style loading process.
Notice when the chief stops, his boots appear to be sucked onto the ground. MagBoots? It would be a way to get some stability in space.
And finally I think the big... thing in front of the chief is a RingSphere. Who knows? it might repair his ship! (Unlikely) It Probably just wants to eat him.