Your GPU is just powerful enough for Ultra, so you're good there. The problem is that Battlefield 4 is a lot more CPU dependant than previous BF games, and your current processor is just a tad underpowered to Max it out.
Also, the BIOS aspect problem is pretty much unfixable, and the only thing you can do is to try it on another monitor. Had the same problem myself a few years ago, but unfortunately Windows BIOS is absolutely resolution locked, and there's nothing that can be done computer-ended to fix the scaling.