What does 식겁하다 mean?
I tried to search it in the dictionary but I didn’t find any details about it.

(1) Is it slang or just a standard Korean word?
(2) Can you use it in formal situations?

Question

What does 식겁하다 mean?
I tried to search it in the dictionary but I didn’t find any details about it.

(1) Is it slang or just a standard Korean word?
(2) Can you use it in formal situations?

Answer

식겁하다 = freaked out 
Its not a slang :)
Korean people like saying “ to eat the fear “ = 겁 먹다 
In the same way, 식겁하다 means the same meaning

Anyway, you can take the meaning as scared in the English way
And you cannot use it in any formal situations :)
The word is too casual basically

Answer

감사합니다 ^^

Answer

(1) It is not a slang. It is consisted of Hanja (Chinese character), 식(eat/have) 겁(frightened) 식겁하다 is like 겁을 먹다.  식겁하다 means that you are surprised and frightened. 
(2) yes.