1. will____you open the door for me?

在此是祈使句表示：征求对方意见请求对方帮忙

2.Why __should__ he think like that?

是特殊疑问句，根据句意应表示：为什么他应该那么想？

3.I _would___ like to make a suggestion.

would like to do sth是固定搭配表示想要做...

4.The window __shouldn't__ (not) open.

shouldn't表示窗户不应该打开

5.You may be certain that the agreement ___would_ be honoured.

是虚拟语气所以用would

6.You know it irritates the speaker when you interrupt;why __will__ you do it? 表示你为何还要那么做?根据时态应选will