I have two questiones.

Not being and English professor, just an average native speaker, the difference to me is this:

"I will go to school." - Focus is on the destination...school.
"I will go to school at 5:30" implies you will arrive at school at 5:30. The main verb in this sentence is "To Go"

"I will be going to school" - Emphasis is more on "going" or the fact you will be traveling, not on the destination. The main verb on the sentence is "To Be".

I apologize, it is not the greatest explanation and as I said, this is just my interpretation as a speaker, not an academic of English.

When someone says 'I have got a cold,' it means that that he or she is *currently* suffering from a cold.

When someone says 'I got a cold,' they are talking about an occasion in the past when they *became* ill with a cold.
e.g.
I had planned to go to the cinema at the weekend, but I got a cold on Friday so I changed my plans and stayed at home.


I will go to school. = 학교에 갈거예요.
e.g.
"What will you do on Monday?"
"I will go to school"

I will be going to school. = 학교에 가고있을거예요.
e.g.
"What will you be doing at 8.30 tomorrow morning?"
"I will be going to school."