[Zigûr]

Being loyal means that he is on Morgoth's side. If he wouldn't be loyal he would go back to valinor and be judged and maybe be turned back into a good guy again. He never did therefore he is loyal.

I don't think the only options for Sauron were either loyalty to Morgoth or loyalty to the Valar/Eru - it may have been that way in the First Age, but afterwards Sauron took a third option: loyalty to himself.

if Morgoth would be in the world Sauron would join him again as a servant WHO LOVES TO SERVE because his master's goals are his own.

I don't think this is supported by Professor Tolkien's own writing on the subject. As has been quoted earlier in the thread, Sauron's goals and Morgoth's goals differed. Morgoth was (certainly by the end of the First Age) a nihilist whose ultimate goal was to destroy the world. Sauron didn't want to destroy it, he wanted to rule it and order it for his own satisfaction. Morgoth's defeat actually made Sauron's desire for rule and order (which he'd had from the start, but which Morgoth only shared until his descent into nihilism) more achievable than it was when Morgoth was around.
While I agree that because Morgoth was the origin of evil in the world, by being evil Sauron was continuing what Morgoth started, it seems to me that the only way that constitutes loyalty is in an unintentional and metaphysical way. The idea I'm arguing against is that he was actively still devoted to Morgoth, which is to say that he was doing what he did to Morgoth's glory or because he believed Morgoth's cause was right. As we've seen, Morgoth's cause and Sauron's greatly differed in the end, so surely as far as Sauron was concerned his activities in the Second and Third Ages were meant to fulfil his own ambitions.

Sauron could do nothing but to keep doing what he did before, what HE IS

What he was doing before, which is to say in the First Age, was assisting in Morgoth's plans of destruction. In the Second and Third Ages he was pursuing his own goal of domination. Surely these are two different things.

A soldier in a army doesn't fight because the general tells him to do so, he fights because he wants to.

I think that's far from true in many circumstances.