need 作为实义动词（也叫行为动词）时,后面接另一个动词,用不定式,need to do,表示“需要做某事”,其否定形式是 don't/doesn't need to do.例如：I need to clean my room.（我需要打扫我的房间.）否定句为 I don't need to clean my room.
need 作为情态动词,只用于否定句或疑问句,不用于肯定句,此时 need 后面直接跟动词原形.例如：I needn't clean my room.（我不需要打扫我的房间.）Need I clean my room?
相信你能看出以上两者的区别.don't need come 就是一个错误的结构.
此外,need doing 表示“需要被做.”,等于 need to be done.例如：My room need cleaning.= My room need to be cleaned.（我的房间需要被打扫.）那如果答案有needn't come 可以选吗？needn't come = don't need to come，两个都正确。