Based on what I've seen so far, the vast majority of the legal challenges to Trump's actions involve laws passed by congress under Article 1 that require the executive branch (Article 2) to do certain things and not do other things.
Simplifying for purposes of discussion, the two main questions are 1) can congress limit the President's ability to fire executive branch employees, and 2) can congress pass laws requiring the President to spend money?
Simplifying (and overstating) for purposes of discussion, the Trump administration has taken the position that any legal restrictions congress puts on the executive branch are unconstitutional, and Trump can ignore laws purporting to limit his ability to fire executive branch employees and laws purporting to limit his ability to spend or not spend money as he wishes.
Here's an example of a case involving question 1 above:
>>>WASHINGTON (AP) — The head of a federal watchdog agency must remain in his job, a judge in Washington ruled on Saturday, saying President
Donald Trump’s bid to remove the special counsel was unlawful. . . .
Dellinger sued Trump last month after he was fired, even though the law says special counsels can be removed by the president “only for inefficiency, neglect of duty, or malfeasance in office.”
Jackson rejected the Trump administration’s claims that the special counsel’s removal protections are unconstitutional because they prevent the president from rightfully installing his preferred agency head.<<<
A federal judge has ruled that the head of a federal watchdog agency must remain in his job, saying President Donald Trump’s bid to remove the special counsel was unlawful.
apnews.com
I'm not sure how the Supreme Court will rule on this, assuming the case makes it there.
This blog post provides a pretty decent overview.
The challenge to Trump's removal of the head of the Office of Special Counsel raises unique procedural and substantive issues likely to prevent it from serving as a referendum—in either direction.
www.stevevladeck.com
I tend to agree that Trump has a decent argument in this case, but it might not mean a whole lot in terms of predicting the outcome of the other "termination" cases regardless of how the Supreme Court rules.
>>>The
Dellinger case. . . raises a constitutional argument in
support of Trump’s conduct that is stronger in
this context than it will be in almost any of the other pending cases. The
Dellinger case is important in its own right. But no matter
how the Court rules, we shouldn’t view the result as foreshadowing everything (or, frankly, almost anything) else that’s coming.<<<