would you like to come to my birthday party?would you come t

用would like to是表示对说话对象的尊重和敬意.而后面的用法应该是will you ...才符合疑问句的结构.
回答的话,第一个是yes, I'd like to. 第二个是yes, I will. （要不然,就成yes, I would了,明显是错误的.）