How can an investor apply for EB-5 while traveling abroad?

Any foreign national, regardless of where they are residents of or currently visiting, can file the I-526 petition.

You may file from any location. You should engage the services of an experienced EB-5 immigration attorney, who will be doing most of the work for you. You should be able to have internet and possibly telephone/Skype access, and the ability to communicate with your attorney and provide legal source of funds documentation to him or her at your attorney's request in order to be able to prepare and file your case in the United States. This should not be very hard.

Yes. You may submit an I-526 petition regardless of your physical presence. There is no requirement that the petition be submitted from any particular location.

You may apply from anywhere.

I assume the I-526 petition will be prepared and filed by your lawyer helping you with this. As we work with clients all over the world, we could easily email all the forms necessary for the client to print out, sign, and FedEx back to us so that we could file. As long as you are traveling to places with internet access and FedEx or some other delivery system available, this is easy.

You do not need to be in the United States to apply.

There is no requirement as to where you file your application.

You can submit the I-526 petition from anywhere (usually, your U.S.-based immigration attorney would be doing it on your behalf anyway). When that is approved, you will need to obtain your EB-5 visa at the U.S. consulate/embassy in your home country.