1----After much effort ,I eventually persuaded him to take my advicethat he_____immediatelly.A.be operated on B was operated onC.operate on D.should operate on2----Much to my surprise,the trapped girl_____stay alive in the ruins for up to seven days with nothing to eat or drink.A .may B.should C .can D.must 3-----People seldom realize that voice needs looking after,many people over 65 are left _______much older than they are.A.sounded B.sounding C.to

1.advice 和 suggestion 之类表示建议和意见的词都是比较特殊的,经常地固定句型都是：sb advice/suggest that ab (should) do sth.某人建议某人（应该）做某事.should 在这里可以省略,但是后面动词要用原形.
所以原题中,that 引导的定语从句修饰 名词 advice 也一样,be operated on 是固定搭配,表示着手做……,should 在这里可用也可以省略,但是后面的动词一定要用原形,所以是 be,综合选 A
2.should 有一个用法是表示（比较强烈的感情地）竟然、居然这个意思,更符合语境；楼主可能选can,如果是自己平时单独写作文的话OK,但是在这里should是最佳答案,比can来说更带感情.
3 首先 感官动词 如sound 是没有被动语态的,虽然我们觉得某个东西听起来怎么貌似是被听,但是用法上是用主动表示被动的.所以排除A.D； be left 伊保持某种状态,如 the light is left on 灯一直开着；she is left sitting there 她一直坐在那.所以类似的 原题应该选 B