Your basic plan is good. You could add more sugar to make it a bit stronger, but that's totally up to you. I've made versions from 4% to 13%.
You will need lots of yeast with nutrients, but will also need to acclimate them to the acidic environment that they will be working in. I make starters for hard lemonade and limeade with a bit of dme, some apple juice, and slowly introduce lemon/lime juice as the yeast is eating the dme/apple juice sugars. (It was either Vinnie Cilurzo or Tomme Arthur who mentioned to make starters with apple juice for sour ales). As far as type of yeast you can use pretty much anything given you grow them appropriately. I've used montrachet, lalvin 71b, cote du rhone, champagne. I am interested in using sweet mead next time.
You shouldn't have a problem with infection from the fruit. I just wash the outsides well with warm water and light soap, then juice goes right into the fermentor.
It will ferment completely out, yes. I have not yet made a batch that is back sweetened (I don't keg, and like to have it carbonated) but I've read that you backsweetening is to taste, but somewhere around 1.005-1.010
One thing I like to do is also add some zest from the lemons. It really adds a nice aroma that doesn't get swept away from fermentation. The last batch of limeade I made, I put in the zest from 10 limes. Lovely aroma.