If a common law marriage is recognized in my home country, how can I add my partner as a dependent on my EB-5 application?

The U.S. does not recognize this type of common laws marriage for green card purposes; you need to have a regular conventional marriage to apply for immigration benefits.

Yes, provided you prove it is a valid marriage in your home country, so prepare all documents to support that.

But it is documented? Like a stable/civil union? That may be OK, but a true common law marriage without anything to show documents wise will be a much tougher ask.

You will need to look at the DOS Reciprocity Schedule for that country and then Marriage Certificate to see what is required.

Yes, your common law spouse can qualify as your dependent if you can establish he or she clearly meets the legal requirements for a common law spouse in the home country. But it may be safer just to enter into a formal marriage.

Yes, include her when the case gets to the National Visa Center.

Yes. If it is recognized in your country that you are so recognize it. You need to prove that you met the requirements for a common law marriage in your country. Whatever those requirements are.