^ It drops because of lag spikes. These can be prevented, as you've seen, by turning down the graphics options. That means that you're producing a minimum of 60 frames every second, so when it drops from 80 to 60, you don't notice it, because your screen can only display 60 anyways.
That being said, don't bother upgrading your monitor. You can go to 1920x1080, which will make everything look much nicer, but a 60Hz monitor is the standard - if you want a 120Hz monitor (allowing you to see up to 120 frames a second) it'll be costly. And there's not much point, since you won't be hitting that 120 mark anyways.
The human eyes have difficulties distinguishing more than 60 fps anyways so 120Hz monitors are overrated if you ask me. It's normal that FPS aren't always steady, you can get variations from many factors like background programs suddenly requiring more resources or simply entering a larger map in the game or having many enemies spawning at the same time, or a lot of projectiles and explosions to manage at the same time, etc...
I think your CPU will somewhat bottleneck your card, but it's still a viable gaming CPU so it shouldn't be too dramatic. Skyrim might just be a more demanding game than I thought and I don't know how CPU dependent it is. I also thought that 35-40 fps were still playable, I always heard that it's from 30 and below that you start having problems. If you want to change your CPU right now most gamers get the i5-3450 or you can also get the i5-3570K for a little more if you want unlock multipliers to overclock. Expect around 50% increase in performance with these new CPUs compared to what you currently have. Also, the 7850 is a very good graphics card, but it's not the most high end either, so at 1080p with max settings it's possible it could struggle in certain games.
With AMD you could get a FX-6300 or 8150 I think both are AM3+ socket so you should be ok. Just make sure you flash your BIOS to the latest version before installing a new CPU.
But I'm not 100% sure your problem is a CPU bottleneck I would like others to give their opinion before you rush to the store. I don't know if it's normal for FPS to drop like that even at low settings... but yeah I think it could be the CPU. It's just that it could also be a software problem, like a bad driver, or make sure you don't have software downloading in the background, or anti-virus doing a scan, things like that. Also, you didn't say how much RAM you have? Make sure you have at least 4 GB.
Makes sense, if you play demanding games at max settings and the GPU never go over 55% use I guess this most indicate a CPU bottleneck. As suggested by maestro0428 you could overclock current CPU and see if the GPU usage increase to let's say 65% or something, then it might indicate that it's really a CPU bottleneck.
I would love too, But im not sure if i could afford a cooler. I spent everything had on this pc
I also have NO idea how to overclock.
Don't worry, I think your CPU can easily overclock to 4 Ghz with the stock cooler especially since your temps are very low (max temp for that CPU is 95C I believe). I don't have a lot of experience overclocking either, but you should easily find instructions for that on the web, especially since you have the black edition it has unlocked multipliers so the process should be rather straight forward, I think it's a simple BIOS options that will allow you to play with the multipliers. Just make sure to watch your temps for stability.