No, it's actually "look upon a woman with a view to desire her has committed adultery already" is what the original Greek text says.
It's not the desire itself but the object of that desire that is adulterous (coveting someone else's spouse). Not looking once, but twice, three times, or more...going back for more of the wrong desire is sin, even if that desire is manifested by looks, or expressed only in thought/fantasy.
The Greek word used is epiqumew which is the same word used in the rest of the NT, such as "with the Holy Ghost sent down from heaven; which things the angels desire to look into." [1 Pet 1:12]
Surely the angels here are not committing the sin although the word used is exactly the same word used by +Matthew.
OK, whatever.
Yes, exactly.