I guess this is possible but I don't know how will this help for the website. Will there be any problems having 2 sites that are hosted with 2 different hosting companies? The site could have 2 different website names. This is not a redirect link but 2 separate sites and have exactly the same content.

No problem at all. It's two totally separate sites.

If the content is not dynamic, then it's not a problem. Unless you're planning on using the second site for a fail over site, I'm not sure what the advantage might be.

If the content changes regularly, then you'd need system capable of updating the 'standby site' with new data. There are some inexpensive methods to keep the content updated, but to do so you'd really need shell access and some server administration experience.

It might be worth to keep in mind that search engines don't like duplicate content, and for most purposes, two identical sites are not really necessary.

It's not quite clear what your goal is in doing this - are you trying to make your site better able to withstand outages? Or just publishing more content? If it's the former, this really only makes sense if you use the same domain name and something like round-robin DNS so that your visitors get directed to whatever site's available. If you're looking to publish more content, perhaps for SEO purposes, the previous poster is correct - search engines don't like this and will likely penalize you for it. It's better to concentrate your effort on one strong site to build up traffic.

I really do not see why there would be any problems with 2 different hosts, but having 2 identical sites sounds like a major waste of money to me. Plus there is the aforementioned problem with search engine listings, and it just seems horribly ineffective and even wasteful to me. Best of luck to you regardless!

There is definitely the issue with duplicate content. Directing visitors to the site with less traffic could be useful, but it might not be worth the hit in search engine listings to do so. But it depends on what exactly you are trying to do I guess.