First manual: Visit the upper floor of Djose Temple. An Al Bhed man will ask you for a password. That password is "MARNELA", named after the matriarch of the Cactuars at Bikanel Desert. Once the password is given, he will give you the manual.
Second manual: Obtained from a man sitting in the room to the left of the stairs in Djose Temple.
Third manual: Walk to the right of the temple entrance. You will find three monkeys in a circle. Stand between the monkeys and wait for all three of them to jump at the same time. Press X to receive the manual.
Fourth manual: Examine the Machina to the left of the crowd of people at the northern part of Mi'ihen Highroad.
Fifth manual: Found in a treasure chest at the Ruin Depths beneath the Chocobo Stables in the Calm Lands.
You can fight and repair the Experiment repeatedly until you get all of its levels up to 5. Once that happens, the Machine Faction will lose control of it and it will be up to you to take it out for good. By defeating it you will receive Magical Dances, Vol. II, which will enable Songstresses to learn the Magical Masque ability.
Special ending: In the farplane at the end of the game after you defeat Vegnagun push X to hear a whistle and a faith appears and asks if you want to see him. You can either pick Yes or itīs better this way. Pick yes and wait till the credits are done rolling to see it.
Perfect ending: Complete 100 percent of the game then repeat the step to get the special ending.
Chapter 2 - Go to Macalania. Look for X-shaped cross on your mini-map (you've just found screen 'Macalania Woods - Lake Road'). NE exit leads to the 'Macalania - Spring' screen you need. You'll find Bayra here (bird with harp). Talk to him and complete 'Track down the troupe' subquest. When you're asked if you wish to board Celsius, choose whatever. If you choose [No.], you'll see Tromell emerge from the woods. Speak with him four times and this Special Dress Sphere is yours. If you choose [Yes.], simply go back down to same screen again, find Tromell etc.
Alternatively, you could do it this way:
Invite Clasko onboard the Celsius in either chapter 1 or 2, and then NOT go to the Calm lands in Chapter 2, he'll get off the Celsius at the Begining at Chapter 3. He will then appear in the Calm lands in Chapter 3 and then complete the 'Clean Sweep' mission.