Benefits from having Facebook page

It depends how you are using your facebook. If you don't want the world to know about, you shouldn't post it on facebook. The disadvantage you list could be eliminated simply by not posting or behaving in a way that would reflect you in a negative light to employers. Or, you could keep your facebook private and not allow none friends to view, if an employer requests an add simply do a "employer friendly" clean up and delete anything you think may affect your job or chances at a job. Then I see no disadvantages, and the network possibilities are clearly the advantage. In my opinion the benefit can outweigh the cons but just like with everything else in life it's all in how you use it.

It depends on you what you require from face book in your website.

The primary benefit of having a Facebook page is to engage in daily communication with your prospects and clients. Keep in touch with posts regarding industry news, relevant articles, tips, videos, photos, etc.

Facebook and any other social media sites can deliver great oppurtunities to enhance a website's traffic. You'll get exposures, targeting your main audience or consumers on your site's services or product. Get notice, create a facebook account.