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Most of the people (if not all) follow the psak halacha of a specific Gadol HaDor. But many times, there are halachot which are not presented by a certain Galdol haDor but by another Chacham. As for an instant, Halachipedia.org does not follow the rulings of one specific rabbi but collects all of them and gives a ruling.

My question is, if I am a sephardi and I follow Chacham Ovadia, and there is a specific halacha not written by Chacham Ovadia but I find it in Mishna Brura or Shulchan Aruch HaRav or any other Askenazi rabbi, do I follow it or just leave that halacha as there never had been any halacha as such? Or in simple words do I strictly follow one chacham or can I change my posek from time to time?

I do not think it is correct that "most people follow the piskei halacha of a specific Gadol Hador". I think most people find themselves a Rav (Pirkei Avot 1:6) and follow him. When they want to learn halacha, they learn one sefer based on the advice of that Rav, who will direct a particular individual based on his specific situation and learning level (e.g., Shulchan Aruch with Kaf Hachaim for a Sefaradi). This way they will know the basic halacha and can ask further questions to their Rav.

When a specific question finds different answers (e.g., certain poskim rule more strictly, others more leniently), a Rav will be able to direct an individual towards the appropriate ruling for him in light of the specific situation and the individual's level.

I don't believe it is ever "wrong" to follow respected poskim such as Mishna Brura, SA HaRav or R Ovadia Yosef, but one should not "pick and choose" a ruling based on the outcome one wants. And ignoring a halacha from Shulchan Aruch because one hasn't found it in the writings of a specific Rav is also not correct.

1. 
   

   Most religious people (at least here in Israel) hardly "follow" anybody - after they finish Yeshivos and got married they basically follow their instincts and learning habits.

   
   
   

   There's a big difference between the Ashkenazis and the Sefardim, as it seems that the A. tradition is much more "developed" in the last centuries and the A. (both Litvakes and Chassidim) feel confidence in Mishnah Berura with slight changes from their personal traditions.

   
   
   

   On the other hand, the Sefardish community was seriously "shocked" by R' Ovadia Z"l approach and Psakim in the last decades and feel much less confident after his death because his legacy is a bit arguable.

   
   



2. As a Sefardi, I would recommend finding a living Rabbi to stick to and following him until you learn the principles and then see #1.