Need advice in building a new PC

In euros that should be about 830. So, somewhat cheaper than you proposed.
My main point is this kind of "multitasking" I described. So if lets say FX6300 does that with no lags, I would be ok with a FX6300. I'm not really looking into overclocking, as I want this PC to be last me about 5-6 years.
So my main concern is, will be FX8350 good enough, or should I consider an i5?

For the tasks that you want to run, and all the open applications, you would be better served with FX 83xx over the six core FX 6300. FX 6300 is recommended for people who are primarily interested in something like mid - high rang gaming as games really don't use more than 4 cores right now. For running as many open applications that you want to, yes the FX 6300 will do it, but the FX 83xx will do it better. I don't know the pricing where you are, but if its not much more (over the FX 8320 I would get the FX 8350 or FX 8370). As for the rest of your build if you want a R9 390 and an FX 83xx you really should get a more powerful psu. For the R9 390 and FX 83xx you really need 700W minimum, and I would recommend nothing under 800W to ensure everything is getting the proper power. Also if your not overclocking (and have no intention to) you don't need a liquid cooler, a cooler like the Hyper 212 EVO is all you would need. I had my FX 8370 overclocked to 4.5Ghz for months (with Hyper 212 EVO) before upgrading to H100i to get higher overclocks.

for both :\

The budget isn't quite fixed at the 8320, but as I read the FX83** are all equal in terms of overclocking, it depends just on your "luck" on the processor your get. So what you're saying an FX8350 or FX8370 will do the job, both gaming and editing ? Is the i5 4670 let's say, going to be much better than the FX's in the same tasks?

``is a Coller Master EVO 212 enough to keep it cold and silent if I overclock it by 200-300hz ``

NO!
get a noctua D14 cpu cooler or other very very good cooler

These guys are right to a point, however there is no support for any AMD FX Series anymore and no future upgrades as well so once this system is done with that means you'll have to drop a wad on a CPU and Motherboard and maybe more depending on what you purchase. AMD as a whole has dropped out of the CPU markets for gaming and such. They were nearly monopolized by Nvidia 6 months ago and were offered to sell themselves to Microsoft also 6 months ago but they are handling things themselves via their GPUs and APUs.

Their FX Series of processors are poor at best for gaming, where even the Intel i5-4440 is par for the FX-8350 but the high core count is decent for editing so there will be a tradeoff. I love AMD, HATE Nvidia and resent Intel as a whole but for this I must say they are a poor option for CPU when you can get a Haswell system with an AMD R9 280X for the same price that is better overall and will have some future CPU availability for a Z97 motherboard. In a nutshell, I strongly recommend you think this over but nothing these guys here say is wrong or incorrect, this kind of decision always has pros and cons when on a budget. With that said, $200 more will really make a TREMENDOUS difference in what you buy and the system's longevity.

You've stated you work on picture editing and things which immediately demands a good GPU which will automatically put you in the gaming zone so no worries there really on budget. With that in mind though it means you'll likely find yourself struggling to justify the cost of CPUs, so your weakest link will be the CPU in your budget. I recommend something that will help the most with the most support and future upgradability.

http://pcpartpicker.com/p/PJZN8d
i5-4440 with AMD 280X will smoke all games at max with 1080p graphics and has DX12 support so its lifespan will last for a few more years high graphics now and possibly high later but plan on medium-high graphics later. My friend has an 8320e with XFX 280X 3GB and he smokes Metro 2033 Last Light Redux and Star Wars Battlefront easily at 1080p high graphics and the card is only $200, so it's very nice for the bargain.

The CPU has only 4 cores, so if you truly need more than 4 for $1300 depending on sales (or less if you wait til after Christmas) you can get an i7-5820K, 16GB DDR4 RAM and the 280X so that'll GREATLY increase the lifespan of your computer while quadrupling performance, where the GPU will need replacement down the road but not the CPU/motherboard since it's a muderhouse of power. http://pcpartpicker.com/p/7nrN8d

Hope this helps, as always, a penny spent is a penny saved later in the life of a computer. If you have the power to wait to save $200 more I'm certain a system like the two above will be very very possible.

(My system has an 8GB R9 390+5820k and nothing slows it down. Converting videos that are 10+GB takes seconds where my old dual core would take over an hour.) My friend uses the 280X with 8320e and runs into lots of microstutter issues but overall it's not a bad buy, for the price however I strongly suggest an i5-4440 or above.

Then I agree, sounds like the OP is stuck between a rock and a hard place. I would say then that the 8320e would be minimum safe bet then but the 8350 then OC'ed would work best. Anything higher than an 8350 is just higher binned 8350 manyway (ie, the 8370 through to the awful 9590 are just 8350's anyway). Less than an 8320 and he'll reget it for games, yes even mid-range games like DOTA 2 will suffer microstutter between the poor core optimization and GPU load. The FX 6300 is barely better than an Athlon II

8350 overclocks higher than an 8320 and FYI the 8320e is not very OC friendly. Chips get hawt, he'll want decent VRM on the mobo no less than a 990fx mobo