What's different about the December 4 US Supreme Court ruling to allow the full travel ban to go into effect?

First, there have been three versions of the "travel ban." The only one that is relevant is the last one, Presidential Proclamation 9645. (Note that an appeals court has found this ban to violate the law as well, but there will be no change in policy until the Supreme Court rules on it.) Many of the references online may be describing previous iterations of the ban, which are not in effect. The US State Department's page on the order provides a chart of who is impacted and an FAQ as to the exceptions and implementation details.

To answer your specific questions:

1. The "bona fide relationship" rule was a side effect of the court challenges and does not apply anymore. However, the proclamation permits consular officials to grant "case-by-case waivers" under various circumstances. Those circumstances (section 3(iv) of the Proclamation) include a number of situations where someone already has ties to the United States:

   (A) the foreign national has previously been admitted to the United States for a continuous period of work, study, or other long-term activity, is outside the United States on the applicable effective date under section 7 of this proclamation, seeks to reenter the United States to resume that activity, and the denial of reentry would impair that activity;

   (B) the foreign national has previously established significant contacts with the United States but is outside the United States on the applicable effective date under section 7 of this proclamation for work, study, or other lawful activity;

   (C) the foreign national seeks to enter the United States for significant business or professional obligations and the denial of entry would impair those obligations;

   (D) the foreign national seeks to enter the United States to visit or reside with a close family member (e.g., a spouse, child, or parent) who is a United States citizen, lawful permanent resident, or alien lawfully admitted on a valid nonimmigrant visa, and the denial of entry would cause the foreign national undue hardship;

   There are other exceptions, including people who already held visas (including those who had visas cancelled under the first order) or were in the US when the ban took effect. It's too early to tell how those circumstances, which would have to be proven at a visa interview, are being evaluated or the likelihood of success of obtaining such a waiver.

2. Whether or not the authorities know you hold Iranian citizenship depends on your history and records, but US citizens are not subject to the ban. For the avoidance of doubt, the State Department page includes an exception for "Any dual national of a country designated under the Proclamation when traveling on a passport issued by a non-designated country." Enter with your US passport, which you're required to do as a US citizen, and you're covered. US lawful permanent residents are also exempted.

3. A lot of news stories to shake your head at and the regular need to contact your Congressional representatives to beg for things. (To word it with somewhat careful bipartisanship.) If you mean at the border, nothing should really be changed, at least in theory, though there has always been the possibility of questions and searches. You might want to read the ACLU's guide, Know Your Rights: What To Do When Encountering Law Enforcement at Airports and Other Ports of Entry into the U.S..