1) Why do we have to leave the copyright notice of VB company on our forum eventhough we paid for the license? and why do they have power to tell our host to take our website down if we deleted their copyright notice?
do webhosting company obey VB laws?

2) Why do we (admins/owners of a forum) get sue by havin infringement of contents in our forum posted by our members? onwers should ignore it?

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When you buy vBulletin you agree to the vBulletin Licence Agreement (found here) and one of the conditions is that you display the vBulletin copyright notice unless you purchase the right to not have to display the copyright.

vBulletin have the power to revoke your licence for violating their Licence Agreement, and if your license is revoked then you'll be running vBulletin illegaly and your webhost will remove it if they find out you're running it illegally.

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And to answer your second question...It is your responsibility as the owner of your forum to monitor all content that is posted there. You are not responsible for illegal material posted, IF, you do something about it/correct it within a reasonable amount of time. If you see illegal material or a copyright infringement and you don't take the steps to correct it, you could be held liable.

It's all measured by what a reasonable person would do....You're not expected to catch illegal material 2 minutes after its created, but if it goes untouched for 5 days, you are doing something wrong. If too many are posting stuff that you can't handle, then you need to either restrict privileges and/or hire more staff.

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Exactly, theres part of the DMCA called Safe Harbor I think, where the owners of websites with user generated content are exempt from legal action because they are not responsible for the content posted, and have the power to remove the content on request

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Let say,
can i post some wordings on the categories description which i think may have or will have copyrigthed material posted by members -

"If you think you are the owner of the copyrighted contents or materials that accidentally posted by one of our members, and we have not delete them yet. Please PM admin or email us with proof that you're the real owner of the copyrighted contents and we will gladly delete the contents out of our website for you."

how is that wordings instead of keep an eyes on all of your websites? let say i have over 30 forums

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Just keep it in the rules that they agree to when signing up. If they break the copyright rules, ban them and report them to their ISP [abuse@theirisp.com]

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You should include it in your rules and wherever else, yes...but the bottom line is that you are still required to monitor what is being posted in your forums to make sure it is legal. If it is illegal, it is your responsibility to remove it.

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How does it work with more contentious issues? For example if some kind of defamation of character post was made and the 'victim' made a complaint. Would you be obliged to remove such a statement before the matter had been taken to court or could you be sued for being seen to be part of the crime?

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I think that your forum postings could be used as evidence if it went to court -but that is highly unlikely

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That's definitely a gray area. There's a very similar incident/lawsuit about it that we've discussed here

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