Invading the mail, on the other hand, is quite explicitly illegal.

The first thing to understand is that one of the basic concepts in our separation of powers system is that the executive has discretion in how it enforces the law. Take something basic like the Sherman Antitrust Act (15 U.S.C. 1). The most important piece is just one paragraph: "Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several States, or with foreign nations, is declared to be illegal..."

The courts establish the precise contours of what is a "restraint of trade" or what is a "combination" under the law. This creates a set of boundaries for the executive. The executive is empowered to enforce the law, but has discretion within those boundaries. If it thinks some class of things is or is not a violation of the law, it is entitled to prosecute cases accordingly until the courts decide the point one way or another or Congress clarifies the law.

Presidential orders cannot create law, but they can guide the rest of the executive branch's enforcement of the law, within those boundaries of discretion. The President might issue a directive telling the DOJ: "we don't think that such and such agreement is a 'combination' under the antitrust laws, so don't prosecute such cases." Usually these interpretations are public (and are published in the form of regulations). Sometimes these interpretations are secret, in which case the media calls it a "secret law." But the key thing is that the directive only guides executive action that was lawful anyway.

Now, the FISA court has been called a "secret court" but it again serves to guide executive discretion, and is not a court of general jurisdiction. Its opinions are binding on no other court other than itself, and its jurisdiction is extremely limited. The basic principle behind FISA is that the executive can do a lot of things as a part of its foreign intelligence function Constitutionally that we don't necessarily want it to do. In particular, it can conduct surveillance of foreign agents entirely without warrants because foreign agents don't have 4th amendment rights. The purpose of the FISA court is to constrain the executive's discretion in this regard, by requiring it to get a FISA warrant for all foreign surveillance, even though such surveillance would not require a warrant under the 4th amendment.

To circle back to mpyne's point: neither "secret courts" nor "secret law" can override public courts and public law. Rather, they are internal to the executive. They guide the executive's discretionary powers within the boundaries established by public law. If they hadn't written it down, they'd still be entitled to do it, and nobody would complain about any "secret laws" or "presidential directives." The things mpyne mentioned are illegal according to public law, and thus not within the executive's power to do regardless of any secret directives or secret court opinions.