Your link is badly out of date - this survey was carried out in May and June of 2003, and first published on the BBC website on Monday, 16 June, 2003.
Things have changed since then - and if I remember rightly,

debated it then anyway - a more up to date survey (this time inside Iraq in advance of this week's elections) is much more optimistic and less overtly hostile to the Bush and the US in general -
Here's a link to another BBC web pageThe full survey results can be found in a PDF link at the bottom of the page - it is an update of a previous survey, which may be the one you linked to.
A majority of Iraqis still want the US and other foreign forces to leave their country, but reading between the lines this is driven more by Iraqi patrioitism than anti-Americanism.
And, when asked in Question 6 "From today’s perspective and all things considered, was it absolutely right, somewhat right, somewhat wrong or absolutely wrong that US-led coalition forces invaded Iraq in Spring 2003?" a small majority - 50.3% - say that the US-led invasion of 2003 was somewhat or absolutely wrong, compared to 46.2% who say it was somewhat or absolutely right, the balance being "dont' knows". This is broadly comparable to the 2003 survey's assessment of the UK's opinons on the matter. And it's a rather wider margin than the one by which George W Bush won his second term this year

.
However, Iraqis seem admirably pragmatic - only 5.7% of them think that the best thing that could now happen to their country would be withdrawal of US forces, well behind 'peace & stability' (19.3), 'security' (33.3%) and just behind 'a better life' (7.6%). (Only 0.4% think that US forces
staying in Iraq would be the best possible thing to happen, well behind the 1.0% for whom a job would be their fondest wish)
In a similar vein, 8.9% think that the 'occupation' forces staying behind would be the
worst thing that could happen, behind lack of security (16.5%), civil war (16.1%), and terrorism (11.5%).
And only 9% or so say that removing US forces should be the first priority of the new government - WAY behind regaining public security (56.6%). Perhaps because the people recognise that coalition forces have a part to play in doing that? It seems so - when asked specifically how long US troops should remain, 30.9% say "when security is restored" against 25.5% who say "now"
There's lots of other good stuff in the new survey (which may well be the one that you were trying to link to anyway
fma), which certainly indicates Iraqis are broadly quite optimistic and not inimically hostile to the US and her allies, though no special relationship should be expected either.
I predict that if & when stable & peaceful democracy does establish itself in Iraq, the people and their government will feel no more obligated to bow and scrape at the very mention of America than the people & governments of continental Europe have done since 1945.
Freedom includes, and must include, the freedom to disagree with one's liberators. If it doesn't, it is not freedom.
But anyway...
What is the reason for the lack of trust for the US around the world?I'd say the number one reason is ignorance. In both directions - many outside America are ignorant about its real motivations and opinions, and assume hostile intent where none exists. And many, if not most, Americans (inside and outside government) are ignorant of the motivations and opinions of people outside America. The latter is talked about more only because America is more powerful than anyone else, so the mistakes America makes through ignorance are more damaging than the ones anyone else makes.
Why is US rated more dangerous than the "rogue states"? How much is the US actions over the last century (arming of human rights violators such as Pinochet) got to do with it? How much of it is purely due to the "War on Terror"?Similar to my last answer, this has to do with America's great power. If I live in Iran, I don't need to fear North Korea because they have no way to do anything to me. America has much greater reach.
Did the absance of WMDs in Iraq affect the public opinion?I'd say that this was most damaging to the US government domestically, rather than internationally, and has to be bundled up with lots of other factors to assess world opinon (e.g. non participation in some international treaties & organisations e.g. the ICC, Kyoto etc.)
What effects will such public opinion have to the world politics?Ultimately, I think the assumption of a
consistently benign America, if it ever existed outside America anyway, will come to an end, to be replaced by the assumption of a spasmodically benign America, when its own interests are helped or at least not harmed. This is more realistic anyway, so I don't see that it will cause any real harm to anyone, though some egos (mostly, but not always, American ones) will get bruised.