To walk is 걷다 (걷습니다).

To go is 가다 (갑니다).

same problem here

갑니다 is present tense but formal. Looking at informal is easier, so if you don't have to add anything special, it's present tense (나는 가 = I go). For past tense, you add -았/었어 (나는 갔어 = I went). For future tense, you add -ㄹ/을 거야 (나는 갈 거야 = I will go).

• Present: 갑니다
• Past: 갔습니다
• Future: 갈 것입니다

I think it is wrong. I would say: 저는 그쪽으로 갈거예요

It won't be wrong in context when analyzed.

However, "I am going that way." would translate to 저는 그쪽으로 가고 있습니다.

"I go that way." does not have present progressive, while "I am going that way." has it.

I said the same thing.