1.
춤을 추다 = 춤추다 =dance dancing (if translate literally)
but it is incorrect so just translate dance
춤을 추다 = dance dancing
왈츠를 추다 = dance waltz
삼바를 추다 = dance samba
so "춤을" is not verb
2.
How do you say "I'll help my grandfather tomorrow"/ "I'm going to help grandfather tomorrow"
I tried this "나는 내일은 할아버지가 돕겠어 "
①. your mistakes
you should use "을/를" after Object
②. your corrected sentence
나는 내일(은) 할아버지를 돕겠어.
③. A casual or native way of saying I'll help grandfather tomorrow
나는 내일 할아버지를 도울 거야.
if use "은" after 내일, it's not incorrect but has different nuance.
just 내일 - i will help him tomorrow (and we don't know today)
내일"은" - i will help him tomorrow (although i didn't help him today)
3.
네가 and 니가 is same and those mean "you"
original form is "네가"
"니가" is dialect but 네가 sounds similar with 내가(means "I")
so many people usually use 니가.
if you want to say formally, use "당신이" which also means "you".