1.Would you please not open(not open)the window? It’s too cold.
解析：would you please (not) do sth. 请（不要）做某事,好吗?
2.Let’s not go(not go)out at the moment ,It’s raining heavily.
解析：let sb.(not) do sth. 让某人（不）做某事
3.He got up late and didn't have (not have ) breakfast this morning.
解析：didn't have 和got up是并列的谓语动词,形式应该相同.