Do you want ___go ___ ___movie ____me?

Do you want to go to the movie with me.

以上答案都是正确的。
want to do sht:想做某事；
go to the movie:去看电影；（固定搭配）
with sb :和某人一起
do you want to go to the movie with me ?
你想和我一起去看电影吗？

Do you want to go seeing the movie with me?
想不想和我一起去看电影？

Do you want to go to see movie with me?
Do you want to go seeing the movie with me? 都正确。
日常口语中还可以用Do you want to go see the movie with me?

to,to the,with绝对是对的啦

to to the with