When the Stark guy knows the King's wife has an incestous affair and suspects her to have tried to kill a fucking child, the guy who loves his wife tells him not to trust him and his daughter tells him about people wanting him DEAD he just claims the Iron Throne without considering that maybe, just MAYBE, he could get arrested/killed.

Im sure he realised there were risks, but the main point is that Eddard always tried to conduct himself honourably at almost any cost. Perhaps there was also some naivety aswell given that the North is largely separate from the political games of the south.

Then there is the dragon girl, who gets married to someone she doesn't love, is raped and then just falls in love with him. Dafuq, Stockholm's syndrome maybe?

Sorta, essentially she had been a helpless pawn of her brother up until marrying Drogo. At this point she realised that the marriage gave her power and the upper hand over her very demanding brother, and she made a conscious effort to please Drogo as well as demonstrate her own personal strength (which also eventually got him killed - by saving the Lamb people witch doctor). While she did this a mutual respect developed, and from that love.

And at the end of season 3 we have other Starks dying because they're complete fools. Marrying another woman when you have already promised to marry the daughter of a powerful ally sure is a bright move, Einstein!

No shit, and it got him and plenty of others killed. The Freys were shown as being a relatively weak house, and Robb essentially thought he could get away with it (The Freys were supposed to be loyal to House Tully [Catelyn's House]. He underestimated the Frey's urge to gain further their own power by cutting a deal with the Lannisters.

a psychopathic teen king who somehow still hasn't died in 3 seasons

Lets just say weddings seem to be unlucky in this series.