If you can give your budget we could possibly give you a good buold to match your requirements. Maximus 4.. that is an old gen motherboard, meaning the cpu you have in mind is also from a previous i-core cpu, the 560 not sure if could be capable, maybe mid, mid-low.
Depending on what generation i7 you have and how many cores, yes it can run Bf4 easily at least medium, probably high 30-40fps.
If it's a first generation i7 with dual cores, probably not good enough, especially for multiplayer. But if it's a quad core i7 you can run it no problem. Your GPU is sufficient