Are the Appointments of Czars Unconstitutional?

First of all, what is the definition of a czar?

According to Dictionary.com:

• A male monarch or emperor, especially one of the emperors who ruled Russia until the revolution of 1917.
• A person having great power; an autocrat: "the square-jawed, ruddy complacency of Jack Farrell, the czar of the Fifteenth Street police station" (Ernest Hemingway).
• Informal An appointed official having special powers to regulate or supervise an activity: a racetrack czar; an energy czar.
  

We can agree that the "czars" that President Obama is appointing seem to fit the third bullet point. With that let me ask? Were these appointments constitutional?

I would love someone to answer this question for me. I have read through the powers of the President. Here is what it says specifically about Presidential appointments from Article II, Section 2:

He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.

There are three points of contention that need to be brought out here:

1. According to this article, the President must have the consent of the Senate in order to appoint officials of any kind, czars ("special aides" with any authority) not excluded. All new positions must go through this process.
2. Did the Senate approve these czars?
3. Did Congress write a law establishing and regulating these positions?

If no, to any of these three points, then the appointment of all these czars is illegal and unconstitutional. Each one must immediately resign their positions! Call them what they like, these appointment are being listed as "aides" but given authority that is not legally acceptable according to this section of the Constitution.

And I am not the only one concerned:

• Senator Byrd sent a letter of caution
• Law professors have asked questions
• Just google President Obama and czars and see what you find (I am getting lazy and set to go fishing with me son)
  

Now, other president have done this, and I question the legality of those positions also. Someone should be asking some serious questions and fast.

• The science czar seems to be a nutcase
• The "pay" czar is fixing to step across presidential authority
• Look at the number of czars being appointed (or here: Obama fashions a government of many czars)
  

Have a great weekend!