Play Halo 4 On Xbox One as a Disc

Just to confirm the current state of things:

Last mission, on ledgenary - half way through

Rest of the missions prior to this: Locked.

Yes, if the game works as Halo 3 / Reach did, each mission has a marker "highest difficulty completed" - the same marker you can see online. The order you complete the missions on won't make a difference, as long as you get the local marker saying each mission was completed on legendary.

However, I'd be making sure you know why the memory was wiped before carrying on - It'd be horrific to play through again only to loose all your progress. All the markers for each mission need to be on the local system - it doesn't matter what it shows online.

Yes, all the Spartan Ops missions are available still. The "second season" is free DLC, so you might have another download if you want to play past the 5th Episode.

All the ops are available in single player, splitscreen, and party play, but the chapters featured in online matchmaking rotate. The experience gain from the online matchmaking is far greater, and you can play with random people on the internet, but otherwise they are identical.