What are the advantages and the disadvantages ?
What about the bunch of quests that are increasing you reputation ? I mean what about the game world around me ? What will change ?
I have rolled the game twice playing with
Keldrorn
Aerie
Jaheira
Minsc
Imoen
Yoshimo
Korgan - I never ended his quest...
What quests I will miss and are there some new ones that I haven't seen yet ?

The advantages are weapons only evil aligned chars can use. The disadvantages are weapon restrictions for goodies. You'll miss some NPC quests but only if you don't take them into your party and gain hilarious NPC quests for Korgan, Edwin plus the Viconia romance!
Playing evil IMO is not that much different from playing good unlike most people think.
There are some quests that can be done to an evil end or with evil actions during the quest (Planar Sphere, Druid Grove, Underdark,...).
Other - so considered - goody quests are no problem for me either. I just snap at the quest relevant people in every dialogue and make it very clear that it's just about the money for me. Keeping you Reputation low (to maintain party balance) is no problem. Kill an innocent! (But be sure there aren't others watching as it will result in a massacre which drops your rep to an extent where you get kicked out of town.
Apart from party balance however there is no bigger point in lowering your rep. Being evil means double if you have a good rep although you have pickpocketed the whole town and killed some innocent children.
So try it the evil way. You'll get a nice Two-Handed and incredibly powerful Leather armor and some nasty quests and miss out on Carsomyr some minor equipment and Keldorn's/Mazzy's/Cernd's "let's run around twon 20 times" quests.

First of all, there is nothing wrong with raising your reputation while being evil. Reputation is the way people think of you, and if you are truly evil, you won't care about people's opinion.

Being evil means you just do what is better FOR YOU, and not what is right/good. Some sarcasm+cruelty is welcome also (IMHO).

Many quests allow an evil way of doing them. Still, you may accept&do the good quest, and be content with the reward it yields. But if the quest-giver does not give you a DECENT reward for your efforts, that was his mistake :grins evilly:

Finally, evil bhaalspawn abilities are better than good. Vampiric Touch yields you additional hps (cast it on yourself and get the boost for free) and can disrupt/damage an enemy, while Cure Light just heals 8 hps.

Larloch's Minor Drain is sometimes usable to disrupt an enemy mage casting, and is a perfect substitute for Cure Light.

Horror is a perfect way to temporary get rid of low-level opponents (and high level also... very useful for my solo kensai).

The only drawback here is the lack of Slow Poison - but you will have a cleric/Periap Of Proof Against Poison, so no problem.

Another disatvantage of an evil char is that he can't use Azuredge, IMO the most popluar and useful weapon there.

Try an evil char, it is worth it!

the Azuredge can easily be substituted with Improved Mace of Disruption

There are some cases where the reputation gained from a quest can be avoided by evil characters. Sometimes it is just that you don't get the rep. point because you were always pestering the locals about getting paid for your help. I think I was able to avoid about half the reputation points in Trademeet this way, without taking any of the "evil" paths to complete the quests.

Also, you can roleplay an evil character with a pretty high rep. Going to 18+ will give you problems with unhappy NPCs, but you can go up to the mid teens without problems. This can make sense from an RP perspective as well...evil characters who want people to cooperate, give them deals at the shops, and not suspect them when they find their gems missing, would be cunning to publicly act as a hero. That way, even if you rob them blind, they would never believe that their hero did it.

--Don't we all know of politicians who do their utmost to keep their good reputation, but whose alignment is definitely not on the good end of the spectrum?

When I play an evil character, I allow them to take into account the benefits of good P.R. when deciding on quests.