Does the Respect required by the children for their parents is equally true for the parents-in-law ? I'm sure a son has to obey his father above his father-in-law if there is any disagreement between them, but except these situations (or parents asking to not follow religious commandments) are they any differences in the relationship? Does a man has to look at his father-in-law as he looks at his father ?
See Shulchan Aruch Yoreh Deah 240:24 where it says that one is m'chuyav to honor his father in law. The passuk where it is learnt from is brought by the Prisha who says that Dovid Hamelech called Saul his father. Whether this is a mitzvah from the Torah is a dispute ,see the Shach who brings the Bach who seems to hold it is a d'Rabbanan .
Some hold that the obligation of honoring parents-in-law is equal to that of parents:
ספר החרדים פ"ה מ"ע מה"ת התלויות בפה, שו"ת התעוררות תשובה א, רכח
However others argue that the obligation is equal to that of other elderly people:
ב"ח יו"ד סימן רמ, שו"ת חקרי לב יו"ד צח
Source: ספר "הליכות בין אדם לחברו" פ"ה סעיף קיד
[Another answer suggested that this is dependent on the argument whether honoring parents-in-law is מדאורייתא or מדרבנן. While those who hold it is only דרבנן (the ב"ח etc.) could certainly not equate it with honoring parents which is דאורייתא, I don't see why it is necessarily true the other way round; just being דאורייתא doesn't mean it is equal to honoring parents.]