What does “scared to pieces” mean?

Does "running down" mean "flowing down"? And please explain the other usage of "running down".

Good question! Although in this context, 'flowing' and 'running' are both verbs, there's a slight difference between the two. 'Running', in this case, is used to describe rapid water or liquid movements. While 'flowing' means more of a steady and continuous movement. Ex: The flood water was running down the street. I love the feeling of Cola running down my throat. The water was running down him.

'Happy' is an adjective, but what about 'that happy'?

In this context, "that" is an adverb meaning "as much as suggested". Therefore, "that happy" means "happy as much as suggested". Ex: She can't go that far.

What's "stone" mean here?

This is a measurement standard for weight that is used in the UK. One stone is equal to 14 pounds (6.35 kg), so the three stone mentioned by Tom Hiddleston in this video here is equal to 42 pounds.

Does the word "move" refers to both verb and noun? Can't I use "movement" instead?

Yes, the word "move" can be used as either a verb or a noun. You could say "movement" instead of "move" here since "movement" is also a noun, however, it sounds better to use "move". "Movement" is normally used when describing the overall action of something moving while "move" as a noun can be used to describe any movement of something more casually. Here's some more examples of "move" used as a noun: Ex: She made a sudden move towards me. Ex: He took his move in the chess game.

What's the main difference between a "lockdown" and a "curfew?" Or are they interchangeable?

They're not interchangeable! Although, you could use them in the same context. The difference is that a "lockdown" can have multiple or different regulations, including a "curfew," and can be implemented for different reasons. It's a much broader term. A "curfew" is when people have to remain indoors during certain times. Ex: Our government implemented a curfew from ten pm to four am. Ex: My parents said my curfew is nine pm, so I have to be home by then. Ex: The building has been on lockdown as a security measure. No one can leave or enter until security has cleared the place.