COre i5 turbo boost

What you are seeing is a program that is coded to make use of a 4 cores. There aren't many. If you run 3d vantage benchmark program , you can watch your cpu change various turbo states. That behavior is correct. If you want to gain speed , productivity you might try to overclock your cpu. You can most likely set it up to run 3.2 in all 4 cores with turbo disabled at stock voltage.

Is it safe to overclock using the motherboard windows interface or I should do it myself in that creepy BIOS thing?
Is it safe overclocking to 3.2 using the stock Fan?

No, it is not safe to overclock any CPU through Windows. Going through the BIOS is very simple, and it won't take much for you to understand what to do.

Your stock fan should be suffice, but I've never used one, so I'm basing this on what I've read. Can someone else confirm this?

I'll walk you through how to turn off Turbo first, then you'll need to post some information on screen. You will want to copy this procedure down.

1. Reboot your system. Before you pass the POST screen, repeatedly press the Del key until you enter the BIOS.

2. Open MB Intelligent Tweaker (M.I.T.).

3. Open Advanced CPU Core Features.

4. Turn all settings to disabled except for CPU Cores Enabled (All), Multi-Threading (this doesn't concern you anyway, so leave it be) and Bi-Directional PROCHOT.

5. Press F10 then Enter/Return to save and exit the BIOS. Your machine will reboot.

6. Re-enter the BIOS and go back into M.I.T.

7. Open Advanced Voltage Settings.

8. Record all of the Normal voltages (the ones in grey).

9. Press Esc until you are asked to exit the BIOS without saving any changes. Press Y then Enter/Return.

10. Post the voltage settings here.

It's perfectly safe to overclock through a program in windows... but has some serious drawbacks. Quite often it is easier to get a stable overclock with changes made to the bios as opposed to using say gigabyte easy tune 6. Also, depending what program you use the settings may not stick after you reboot if you use a OC program. If you overclock in the bios the settings will take effect every time you boot your pc.

3.2 should be fine on stock fan if you don't change voltages or raise the core by one notch. This may not be the case though so it is critical to keep an eye on your cpu temps AT FULL LOAD. With the i5, aiming to keep the temps under 60c is a good goal.

I overclocked it to 3.0 Ghz through the gigabytes utility in windows and using the stock fan. when it works full load the temp goes to 85 C for maximum.
sometimes the computer gets shutdown for no clear reason. could it be about cpu temperature?

I would be concerned about 85 temps, the performance gains from 2.66 -2.8 turbo to 3.2 overclock is not worth damaging your chip in my opinion.