Hi Priscilla, great question! "carved-out block of time" simply means scheduled time. This text is talking about scheduling time to relax and go see a movie. Another way you could use this expression is to say: "I am very busy tomorrow, but I can carve-out some time to have tea with you." You can see that it really means the same thing as "schedule". This expression is certainly used in American English, but I am not sure how common it is in other English speaking countries.

It means that there's a period of time that he gets to watch a movie in, it implies that he gets to be by himself or enjoy some relaxation that is allocated because when you're in a movie you're not getting interrupted, for example. "Carving out" time is a somewhat common expression meaning that you fit something in or allocate time for it in a busy schedule. To carve as a verb- like you might carve meat or stone, you cut it up.

he is referring to the allocated time in which he would be watching the movie and nothing else