Head to the Huerta Memorial Hospital to find an asari outside insisting over the phone that, if only she had the Rings of Alune, an artifact sacred to her people for reminding them of the importance to helping one another, then maybe more asari would be willing to help out in the hospitals aboard the Citadel. You will have to head to the asari’s area of the galaxy, currently infested with Reapers, to find the planet that the Rings of Alune are located on. Get in the Normany, fly to the Silean Nebula. From there, visit the Teyolia system, and scan the planet Nevos. You will find the Rings. Bring them back to the asari for your reward.
You will have picked up the Library of Asha quest from an asari standing by the steps in the Purgatory club. She will be complaining that her people are more exotic dancer than warrior nowadays, and that where they are really needed is on the battlefield challenging the Reapers. She wishes that someone could get the Library of Asha to help train new warriors. Head to the Nimbus Cluster, then from there the Agaiou system. Scan the planet called Carcosa to find the Library, and return it to the asari in the club to collect your reward.
To get the Valhalland Threshold: Prothean Data Drives side quest, head to the Alliance soldier talking with the asari in Docking Bay C-24. To get the Data Drives, head to the Valhallan Threshold, the Paz system, and the planet Garvug. Scan the planet and return the spoils to the soldier in the Citadel.
Head to the Docks: Holding Area section of the Citadel via the elevator, and find the colonist talking to the turian C-Sec official by the lobby. They will be located near docking bay E28. The colonist will say that there is a Prothean sphere-like object on a planet called Gei Hinon, located in the Hades Nexus, and that this is some sort of valuable technology that could be of use in building the Crucible. The human will try to sell the specifics of the information to the Alliance. Head to the specified location, in the Sheol system, and search Gei Hinon for the sphere. Return it to the human to receive your reward.