> 2. There can be arbitrary changes to law too, with a change in power.
Arbitrary changes to law aren't retroactive in general. If you did something in the past that has later become illegal, you can't be prosecuted.
The same doesn't apply for policy changes.
There is no prohibition on the legislature passing civil ex-post-facto laws, only criminal.
Agencies can only enforce ex-post-facto policy changes if congress explicitly authorized them to.
... Also, as Matt Levine points out, executive agencies are prohibited by law from making capricious and arbitrary policy changes. Congress is not bound by any such restrictions - it can pass legislature that is as capricious and arbitrary, and as completely devoid of public input as it likes.
Arbitrary changes to law aren't retroactive in general. If you did something in the past that has later become illegal, you can't be prosecuted. The same doesn't apply for policy changes.