1. Brake drag:
That model R6 has always been notorious for front brake drag. I spent hours getting that system to work halfway decent. If your willing to spend the time, here are some things you can do.
First take the pistons out and polish them.
When you re-install, use permitex caliper piston grease in the grove of the seal and spread on the piston face as well.
After you've got everthing back together leave the calipers off and work the pistons back and forth (this is easier with the pads installed, make sure to put something in-between the pads of the caliper you are NOT working on to keep the pistons from popping all the way out) by pumping them out with the lever and then pushing them back in. After a while you should start to see them retract when you release the lever, now your brake drag should be minimal.
remove the pads and wipe off any excess piston grease to avoid attracting dust/dirt.
In the future - Do not use brake cleaner to clean the calipers and pistons as it dries out the seals. Use something like WD-40 or some guys like simple green.
Bleeding the system:
Sounds like you have air some where and/or probably need new pads. Like someone said above try bleeding at the banjo bolts but tip the caliper so that the banjo bolt is facing up. Sometimes a stubborn air pocket will be in the top of the caliper cavity and it will come out if you bleed from the banjo with it facing up. You could also try putting a rubberband around the lever and handle bar over night, this will sometimes get stubborn air bubbles up to the MC reservoir. Repeat, repeat, repeat.
You probably need to replace.
Can't remember if these are torx type or allen but the best way I've found to remove either is an impact driver (the kind you hit with a hammer) otherwise you will most likely round the head of a few (which turns your project into a nightmare). I have had to use heat on some in the past as yamaha uses a ton of locktite. They are torqued to a very low spec, something like 13 lbs. if I remember correctly but a real bitch to get out the first time. I have not used locktite on re-install and have never had a problem.
Maybe, but I'd work on the other stuff first (bleeding and pads) they are cheaper.
Hope this helps, feel free to pm for my number if you have questions or need more detail.