- What profits Accrued by US from this alliance?
USA gets to prevent Saudi Arabia from becoming a part of, or a vassal state of, a powerful OPEC neighbour (Iraq or Iran), which, while less rich, can dominate KSA militarily.
That, in turn, keeps the oil price lower, by keeping an independent money-hungry Saudi dynasty with a control of a wide oil spigot, meaning Iran or Iraq cannot by themselves enact an effective oil supply squeeze
That's pretty much it. The actual, real, choice available to USA is not between a nice democracy controlling Arabian Peninsula vs the oppressive monarchy. It's between oppressive monarchy of House of Saud, and the oppressive regime of (Saddam Husein|Ayatollahs: pick one) controlling it. In the real, second choice, the house of Saud is a much better outcome to USA, geopolitically.
How US politicians Justify this alliance to people of America and world (what excuse)?
Largely, they don't. Most Americans are extremely unaware of either the nature of KSA internal politics; or US's exact relationship with the regime, even after 9/11. And those few who are aware either already oppose the relationship (and thus would not buy the justifications, anyway), or have realpolitik views as outlined in my answer to your first question and don't need justifications above that.
Additionally, for the last 28 years (Bush 1, Clinton x2, Bush II x2, Obama x2) USA had presidents who pursued foreign policy that was wholly independent of what the country's popular opinion wanted, in large part due to their views of the supremacy of executive power, no matter their actual policy positions.