Dick move by Fox and Singer in throwing in Quicksilver, clearly last minute after Whedon all but officially confirmed him in A2. I'm a little annoyed but all in all, when the audience compares the X-Men Quicksilver to the MCU Quicksilver, it's going to be an embarrassment for Fox. I also don't think the DOFP Quicksilver is going to get much screen time, and if they'll even call him by name, so not sure it's really going to put a dent in Whedon/Marvel's plans.
As for how rival studios can both use the same character, Marvel Studios can use him and Scarlet Witch so long they don't refer to their mutant lineage. It's certainly going to be a bit confusing to the general audience but if my theory is correct and Quicksilver is going to be a bit character in DOFP, it's not going to matter much except to the hardcore fans.
Btw Quicksilver already had a quick cameo in the (terrible) Wolverine solo, and the Fox continuity when it comes to mutant appearances is effed beyond belief already, so I think the general audience really won't care.