Can I say “Sorry for that” instead of "sorry about that"? Does it mean the same?

What does 'sort of' mean?

"Sort of" means in some way, slightly, somewhat, moderately or like. Ex: She sort of has a crush on Jimmy. Ex: He sort of likes the Avengers movies.

Does “don’t wander far” mean “don’t go away and stay here”?

To "wander" means to walk around casually or aimlessly, and "don't wander far" means don't go too far away. She says "don't wander far" in this case to imply that if they start to walk around and get too far, they might miss the samples that she has. Ex: It's busy today, don't wander far or you might get lost.

What is the meaning of "mischief"? Is it same as "prank"?

"Mischief" has a similar meaning to "prank," but they are slightly different. "Prank" refers to an actual trick or joke (which can be harmless or playful), whereas "mischief" refers to sneaky or troublesome behavior (usually negative) in general. Thus, a "prank" can be considered to fall under the category of "mischief." Ex: I played a prank on my dad yesterday. Ex: The kids were up to mischief again. They spray painted vulgar words onto somebody's car.

What's "emanate" mean and when's it used?

To "emanate" is a verb that means something coming out of a source or origin, usually something abstract or able to be noticed. Ex: Joy emanated from his face. Ex: Warmth emanated from the fireplace.

Is the expression "lead to" always used to refer to something negative?

No, the expression "lead to" does not always refer to something negative! The general meaning is that one thing causes something else to happen or exist. So that could be negative or positive. Ex: Sometimes evaluations at work lead to getting promotions. Ex: Breaking the rules can lead to getting detention at school. Ex: Being kind can lead to good things happening to you.