these men to arrive是动词不定式做后置定语

2.Just the fear of them settled the argument in favor of Luke Short.

in favor of赞同,有利于

例句：I have decided in favor of this plan.
      我决定赞成这计划。

3.Bill Tilghman pulled out his gun and shot Ed Prather two times. He died immediately.

pull out退出

例句：The invading troops are pulling out of the occupied area under international supervision.
      入侵部队正在国际监督下撤出占领区。

拔出

例句：The drawer won't pull out.
       这抽屉拉不出来。