A quesiton about "be going to"

"I am going to the park tomorrow."
"I am going to go to the park tomorrow."
Which one is right?

The first one is an arrangement, indicating that it is quite fixed in some ways and you don't expect it to be changed. eg. I'm sorry we can't meet in the morning because I'm going to the park tomorrow. It is usual to use this tense (pres continuous) for appointments especially if they involve other people.

In the second one you express a plan- ie some kind of premeditation or preparation. It's not something you have just thought of. eg. I want to start to take more exercise so I have decided I'm going to go to the park tomorrow.

Notice that in the first you have to say the time (tomorrow) to show it is future otherwise it may be taken as refering to the present. In the second the time can be omitted and the future meaning is still clear.

Also mention that often in spoken (at least European) English the second one is often abbreviated to the first because it is shorter and the repetition of 'go' is a bit clumsy.

A quesiton about "be going to"

"I am going to the park tomorrow."
"I am going to go to the park tomorrow."

Which one is right?

Both are correct.  However the meaning is quite different.  In the first sentence, "going" means the act of moving to that that place.  In another words, you have started moving already.

In the second sentence, "going" is not the literal meaning of "moving".  You are "moving" in your thoughts.  Here this "going" means "thinking".  In other words, you are are about to go, not started yet.

"Where are you going?"
"where are you going to?"
Are they different?

No difference in meaning for the above two sentences.  In speech, the 2nd one is considered more polite.  The first one sounds abrupt.  However, in writing, the first one is deemed more "proper"

Thank you for your help.