All these actions legal to apply within my website?

All of the items you list are currently being done by other sites, so there is a proper way to legally do those things. You will need to consult...

Can my Brother in Law sue his competitor for a false website that reroutes users to the competitors website?

According to what you have listed above, there are several different potential causes of action available to your brother-in-law. He will need to...

Can scientists claim another's work, solely based off the fact that the research was conducted in another scientist's facility?

The simple use of another person's facility does not prevent you from claim ownership of your work. The ownership of intellectual property is...

Can I copyright an eBook of art and then publish art individually?

If you file a collection of photographs as one copyright application, the copyright will be in the collection. If you want to protect individual...

I would like to add pictures of artists (who have been dead at least 50 years ) to my self published e-book for sale on my site.

The right of publicity and copyright law are tricky areas. You will need to consult an IP attorney. In addition, right of publicity laws are...

If I file for a Trademark in the US, will this protect me in the entire world, or is this specific to the US?

A U.S. trademark registration is only effective in the U.S. If you need protection in other countries, you should seek registration in those...

Does anyone have a patent right, to patent a shape? For example a handle that's Octagonial in shape.

You would not be able to patent a shape, absent its connection to a useful article, and even then, the shape itself would have to impart some...

I am switching this to Criminal, so you can receive responses from the appropriate attorneys.

Designing

You will need to determine what intellectual property Reinast has in order to determine your risks.

Do my local patents apply only in terms of territory of producing the item, and can I sell it worldwide without concerns?

A U.S. patent has no effect on selling or manufacturing outside the U.S. It does protect against importation of infringing goods into the U.S. If...