1.He found a house was on fire,so he jumped out of bed and called 119. jump out of bed不用加the,因为不需要特指某张床
was可以去掉,也可以留着,如果留着was的话,就可以理解为是省略了that的宾语从句；如果去掉was,就是一个简单句,所以was在这个句子里应该不是主要问题.
2.They praised Jack who had already put out the fire. 加上who变成定于从句,语法上就没有问题了
3.They thanked him. 因为这里需要用宾格