Yes the US violated its own laws. There's not really a "legitimate" (or inside the bounds of the law) way to break the law. I guess you could say it all eventually got made legitimate because, historically, any cases that made it to the Supreme Court usually resulted in the court reading/applying the constitution in a way that made the US come out on top.

There's no simple remedy on hand to deal with any legal cases that arise. In 1946, Congress set up the Indian Claims Commission which allowed tribes to file claims against the United States. They were mostly land claims that resulted in some financial compensation. Getting actual land back was extremely rare. The ICC ended in 1978.

I think the majority of cases that get brought against the US these days have to do with tribes fighting for federal recognition after various termination policies. Cases involving treaty issues tend to involve (but not always) states violating the treaty rights. The bigger cases that have strengthened tribal treaty rights that come to my mind at the moment resulted from a state pressing charges against individuals, not tribes filing lawsuits over violations.

It's an extremely complicated matter so that was all oversimplified but I hope it answered some of your questions.

One thing to keep in mind is that the "treaties" in question, really were a multitude of different agreements with various levels of legal standing, made between actors as diverse as the Federal government, State governments, local municipalities, and even private individuals. The closest we come to the US, as a singular actor, breaking treaties would probably be the 1871 Indian Appropriations Act, which changed the status of Native American groups from sovereign (if not equal) nations to non-sovereign dependents. This set the stage for the break up of tribal lands, most notably through the Dawes Act, which privatized and sold off those lands in allotments. Ostensibly, the Natives living on those lands would buy the allotments, but in practice large swathes of what had been Indian Territory went up for sale to homesteaders.

There's a whole history of malfeasance and/or incompetence by Indian Agents and the BIA. Sometimes treaties would be signed with individual groups, wherein they gave up territorial/resource rights in exchange for remuneration and support from Federal/State governments, and those payments simply never happened even as their lands were occupied. The 1868 Treaty of Fort Laramie and the 1851 Treaty of Mendota are both examples of much being promised and little being delivered, and both with violent consequences.

If you're interested, there's a comprehensive, if dry, book on this topic: Prucha, FS (1994) American Indian Treaties: The History of a Political Anomaly. A more accessible case study I would recommend would be the quite good This American Life episode on the Dakota War, which stemmed from the Treaty of Mendota, among other factors.

I've love an answer to this as well. Cobell vs. Salazar was one example where a vast number of individuals received moneys based on the non-payment and inadequate payment of lease moneys and other income from Indian land held in trust by the BIA.

I think for the most part, tribes try to fight for their treaty rights piecemeal. The fight for fishing rights guaranteed by treaties to northern tribes often resulted in violence against Native fisherman. Sohappy v. Smith helped guarantee those rights in the 1970s—that named the State of Oregon as a defendant.

Walter Echo-Hawk advocates using the UN Declaration of Rights of Indigenous Peoples as a tool to convince the United States to honor treaty rights. You might check out his book on the subject, In the Light of Justice.

Are you familiar with the Native American Rights Fund (NARF)? They are a coordinated, intertribal effort to fight for Native legal rights.