your current resolution is fine. 1080p is perfect for that card. Only when you go with a bigger sli setup or a higher end gpu do you have think about getting another monitor with a bigger native resolution.
99 percent of LCDs can only spit out 60fps coz the run at 60mhz. So that why I say you will only see 60fps. So can you see what will happen when you run something like 2 or 3 cards but your monitor limits you? But that's not important now coz your resolution you have is perfect for that card.
For the overclock question no the gpu and cpu clocks have nothing to do with each other. If a cpu bottlenecks it means the cpu can't keep up with the gpu normally as it is too slow.
Reasons its too slow can be
1. You got a very old cpu, which you don't have
2. Your running at gpu at a very low resolution like 720p when it can handle 1020p with ease. That's not a issue coz your running it at a high resolution.
3. Your have a low clock speed. Now its well known all round running a cpu at 3Ghz and above get rid of any cpu bottlenecks. Some games are less demanding on the gpu and a cpu with a higher clock will mean the gpu can't pull away from it or if the game is cpu intensive the cpu won't trip in its own workload.
When you overclock you'll have to overclock the fsb. There are numerous overclocking guides here's 1
http://archive.atomicmpc.com.au/forums.asp?s=2&c=27&t=1&p=0
You can google and you'll find lots of them