I'm thinking on replacing my old speakers which are for Hi-Fi application (due their tweeters are horrible, alrought it reproduces well even the 30Hz because it was made long before the age of subwoofers), with the possible option of getting studio monitors instead.

I'm have some knowledge in electronics and so far I know that even my integrated amplifier (which is a Pioneer SA-770, newer models lack features like a simple EQ, input selection) is good enought for driving studio monitors. However, most studio monitors I see on the market have integrated amps.

And yes, I want to also use them for listening music. I already using my monitor headphones (Audio-Technica ATH-M40fs) for that, the only downside is that it's impossible to listen Metallica's Death Magnetic throught it because the distorted mastering is even more obvious.
I don't see anything wrong with passive studio monitors. All studio monitors used the be passive and it didn't stop people making great recordings.

You could also have an active sub with them. Look at KRK for example.

Keep the speaker wires short and thick.
Yes, passive monitors exist and are fine. Some of the most famous monitors, Yamaha NS10s, are actually repurposed hi-fi speakers that require an external amp (I personally hate NS10s but that's just me).
Current Gear:
LTD MH-400 with Gotoh GE1996T (EMG 85/60)
PRS SE Custom 24 (Suhr SSH+/SSV)
Ibanez RG3120 Prestige (Dimarzio Titans)
Squier Vintage Modified 70s Jazz V
Audient iD22 interface
Peavey Revalver 4, UAD Friedman BE100/DS40
Adam S3A monitors
Quote by Anonden
You CAN play anything with anything....but some guitars sound right for some things, and not for others. Single coils sound retarded for metal, though those who are apeshit about harpsichord probably beg to differ.
Mine are passive. Yorkville YSM-1.

Careful, though... I have an active sub, but it doesn't drive the monitors. It only powers itself.

Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.