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What country are you deploying the logo in?
As far as copyright is concerned, in the UK at least, copyright is automatically assigned to the creator of the work be it graphic, literary, music etc, etc...
1/2. Registering and trademarking is usually handled by government departments. In the UK, it's
http://www.patent.gov.uk/
3. You can't. Well, you can't be
absolutely sure. No one can. Even if two companies get involved in a dispute over logos, the courts will probably decide the outcome. In my experience, two companies who have roughly similar logos can co-exist providing they are in different spheres of operation e.g. Toiletries and DVD Sales outlet. The courts would decide whether the public could be confused by the mark. In most cases, it's quite unlikely.
Finally, I'd say that if you've got any niggling doubts about a logo infringing another mark, it probably does!!! :)