Sorry it took me so long to respond. Completely forgot about your post. I see some of your questions have already been answered. So, here's what happened: While Master Chief was off at Delta Halo, Blue Team (Fred, Linda, Will) was fighting the Covenant on Earth, going on a multitude of missions to stop Covenant digs and interrupt their operations. During this, Lord Hood received a message from Dr. Halsey (who had kidnapped Kelly prior) stating that there was Forerunner tech at Onyx that could turn the tide of the war, and she needed Spartans to secure it. Blue Team was given the order to get to Onyx. They hijacked a Covenant ship and landed at Onyx. There, they met up with a handful of SPARTAN-IIIs, Kurt, Kelly, Dr. Halsey, and CPO Mendez. In the process of accessing the Shield World at Onyx, many of the SPARTAN-IIIs were killed along with Will and Kurt. The survivors accessed the Shield World and Onyx was destroyed. The surviving Spartans were all designated as Blue Team members. In 2553, ONI located the slipspace bubble containing the Shield World. After conversing with the survivors inside, they were able to bring the Shield World into real space. From there, the survivors were rescued, except Dr. Halsey who was arrested for war crimes. From there, Blue Team from there would be broken up and downsized to just Linda, Kelly, and Fred. From there, Blue Team went on a series of classified missions, rooting out remaining pockets of Covenant Loyalists, and quelling the insurrection. In July 2557, the Master Chief would be asked to advise Blue Team on a mission to investigate the loss of contact with Black Team and the science team on Installation 03. Arriving at Gamma Halo, they would find that the composed souls of New Phoenix's residents had been transported here, and were being sent through a service portal to the Composer's Forge. Arriving there, they would find the Didact, who had begun to amass a multitude of Composers to finish off humanity. The fight with the Didact would be perilous, with the Master Chief suffering considerable damage and injury. The only reason they survived was with the help of 859 Static Carillon. The Master Chief came up with a plan to use the composers against the Didact, and he successfully defeated him. The Didact is currently considered contained. From there, the Master Chief would be reinstated with Blue Team, and would go on a series of, as of yet, classified missions.

[quote]1. How are they still alive? Did they magically warp off of reach when it was decimated or was there some forunner wizardry at hand?[/quote]A handful of SPARTAN-IIs that survived landfall and the subsequent Covenant assaults, made there way to CASTLE Base, where they took refuge with Dr. Halsey. The Master Chief and co. returned to Reach to look for survivors and found the Oly Oly Oxen Free code being played. Knowing some of his team mates were alive, the Mater Chief rescued them. After conducting Operation: FIRST STRIKE, they returned to Earth. [quote]2. Linda DIED. There was even an easter egg about it in Halo CE Anniversary. How could she possible still be around.[/quote]She was clinically dead. The Chief put her in cryo with the possibility of her being revived by skilled medical professionals. Before the Autumn crashed on Alpha Halo, it ejected any remaining active cryo pods into space. After Halo's destruction, the Master Chief and Cortana picked up Linda's Cryopod. Dr. Halsey, with the aid of a flash cloning kit, was able to successfully revive Linda.

They trick the Ur-Didact in to composing himself. He is technically still alive and it is unknown if he still poses a threat to humanity. Halo Escalation takes place a few months after Halo 4 and that proves Blue Team is still active (including Linda)

Ok then.