I don't think they lied to him, however, there's a twist in their words (demon promises tend to be treacherous), he wouldn't feel sorrow and despair towards his wife. He only sacrificed her, and so his wish as towards her actions and his as a result of those. So, the despair he felt on that scene and sorrow for killing his own wife would never torment him again.
And this, I believe, is the answer to your questions no. 1 and 2, he only lost "half his humanity" or so to speak. His daughter was the only other person he cared for, and she clearly could still burst him emotions even in his demon form, as a trace of his remaining humanity.
"So as a demon he shows more compassion and restraint than as a human"
Hmm, no? He is described as a fair ruler in his human form, and also religious if I recall correctly. Thus, seeing his loved wife amidst herectics, he could not keep his sanity. Two different questions mixed up pretty bad here, first the whole scene is completely unacceptable, second, his wife was taking active part on it - sharing the intimacy only he had with her.
As for the third question, that's very theoretical. As his wish as to defeat Guts, probably a stronger body would be granted to fit that goal, but even that could just not be enough. How to completely guarantee that?