When a man is in prison in China I can do no 'work' as you put it to help him.
I might give money to THE church in China if there was a means to do so .
But you are mistaken if you think prayer is not a work . For it can be a work of sweats of blood it can be a work of great travail and pain as of giving birth .
As Far as I am aware Jesus never publicly prayed for the sick. he prayed in secret and the Father answered publicly .
In John chapter 8 we read of the account of the woman caught in adultery . But the story starts in the last couple of verses of Chapter 7 , Where while every one "went to their own homes" Jesus went up to the mountain to pray.
You are right that faith without works is dead and we should were possible put legs to our prayers.
and walk and work in accordance with our praying .
But when James the Apostle was put in prison and then put to death .perchance not much praying was made for him ? with the idea that he was an apostle and nothign could harm him?
When he was executed and then Stephen when Peter was put in prison and ready for execution .THEN they all began to pray as if his life depended on it . Did they do a work? or was it God who did the work?
They did nothing other than pray.
We must pray as if everything depended on God . It does .
We must work as if everything depends on us .,It does .
Paul spoke about doing a 'work' when while he was not present he was with them in Spirit and had already given the guilty mans body to the devil so that his spirit might be saved.
There is a whole world to praying that we do not yet know but which the scriptures lay out for us to encourage us to be more effective in our prayers .