Immigration court is a different situation than other courts in the United States. You do not have many rights as you do in a typical court.
The high-stakes nature of these court cases means it is essential that you understand what rights you do have and how to accommodate for the ones you do not.
The reason for fewer rights
You may not have some rights in immigration proceedings because these are civil and not criminal cases. The U.S. Constitution only guarantees certain rights when you are facing criminal charges. Civil cases within the U.S. judicial system usually carry lighter penalties and are not as life-changing as criminal cases. Still, immigration issues are the exception. They can impact your life, but the way the system categorizes them is still civil.
Specific rights you do and do not have
In general, you have many of the same rights as citizens because the U.S. legal system treats everyone equally. You have the right to due process and equal treatment. The biggest difference is that you cannot get legal representation for free. In addition, while you have the right to a speedy trial, immigration courts are typically very slow, so it may not be as speedy as it should be.
The bottom line is that you should expect to get fair treatment when going to immigration support. You have the basic rights afforded to anyone within the legal system. Just be aware of the slight differences and how it being a civil matter may impact your rights.