Only full numbers show up as %, ie 1%, 2% etc. %'s such as 1.6% won't show, it'll stay as 1% untill you reach 2%.
It is important that you find and 'talk' to that Moogle during the mission. It is only supposed to heal you but later in the chapter it opens up another mission in Luca, and reveals who the Moogle really is.
If your going for 100% and are following a guide, do exactly what it says. I suggest having two files. 1 file as your going along and a 2nd file as a checkpoint. Use your 1st file as you normaly would and once you reach a full percentage after a mission or something and it is the right percentage as shown in the guide it means your doing it right and should save on the 2nd file. Carry on, only saving onto your 1st untill the next point where you should have a full percentage complete as shown in the guide. If the percentage is wrong then you have done something wrong and should reload from your 2nd file and redo, trying to make sure you do everything.
And yes the Sphere break tournament does, seeing as you also get the Lady Luck dressphere for winning as well as a scene.