There are 3 side quests. Malcom's Will, Altar of Dumat, and The Paragon's Heir.
Side Quest #1 Malcom's Will
This quest begins on the first floor (Sashamiri's Floor). You will see a shade locked in a magical prison. You must free him and then kill him. In order to free him to must interact with 2 magic trigger points (red dots) in the area once you have activated both, go back to the magic cell where the shade is captive and activate the 3rd trigger point. Once the shade is free he will summon replications of him self and attack you. Defeat them and the quest will be added to your journal.
The 2nd magical prison is on the next floor (Farele's Floor). The 2nd prison is on the eastern side of the floor. Once the 2 magic trigger points are activated go back to the cell to activate the 3rd. This time you are fighting an abomination and profanes. Dispatch of them and the quest will update.
The 3rd magical prison is on the same floor as the 2nd prison (Farele's Floor). The 3rd prison is about half way through the floor on the northern side of the map. This time you are fighting a desire demon that will summon corpses and skeleton archers. Dispatch of them and the quest will be completed.
Side Quest #2 Altar of Dumat
This quest can be started on the 2nd (Farele's Floor) or 3rd floor (Tower base). This quest is started when you pick any 1 of the 4 artifacts in the tower. The quest can be finished 1 of 2 ways, either you defile The Altar of Dumat (requires only 1 artifact) or you can perform a ritual to honor Dumat (which requires all 4 artifacts). You only have the option to defile the shrine until you placed all 4 artifacts. Once you have placed the 4th you are locked into performing the ritual. There are 2 artifacts a piece on the Farele's floor and Tower base floor.
If you want to perform the ritual here are the locations of the 4 artifacts.
The Crown of Dumat is found in a side room on the eastern side of the floor.
Dumat's Sacrificial Dagger is found in a side room on the western side of the floor.
Dumat's Ritual Scroll is found just north of Dumat's altar. There is a set of stairs creating an L shape. The scroll is on the upper platform.
Sacred Urn of Dumat is found in the clearing after the area in which the Altar of Dumat is located (in the Tower Base). It is in a small cave just to the south of where Hawke battles deepstalkers and spiders. This beyond the altar, so you your first encounter with the altar you will only have a max of 3 artifacts.
Side Quest #3 The Paragon's Heir
This quest begins and ends on the 3rd floor (Tower base). The quest is started by finding the 1st Legionnaire's journal which is on a dead-end path to the south of the first main clearing. The second entry is in a large submerged stone building to the north of the second main clearing. The third and final journal entry is in a small cave just to the south of the next area after the clearing where Altar of Dumat is located.
Once you have all 3 journal entries a map marker will appear showing you where Garen Tethra's body is. Its East of the 3rd journal entry. Its off to the right, right before the stone bridge. Once you have found the body the quest will be complete.
Here is a map for references on where the journals are and where Garen Tethra's body is.