Ken has asked me to advise on this Occlusogram so I have decided to share it on the the Forum 
1) what is the sequence of alignment of the upper right quadrant in order to gain mesial movement of 16 and correct the class III molar to class I molar relationship?
I would start correcting the mesial rotation of the molars with a TPA, ad a straight segment between 16 and 15 and a RLoop between 26 and 25, add also some expansion.
Once this is fine align 12 with RLoop and add a C. with from 26 to midline to prevent incisor lingual displacement. After this, you should have 2 maybe 3 mm space between 12 and 13,
To mesialize teeth 13 to 17 I would recommend you to use Tad's. I usually would put one to block 26 and the TPA to mesialize on the right side, maybe you also need another tad on the buccal rigt side. Buccal mechanics can be also used together with TPA with T loops or cantilever with configuration.