1. Life and literary activity of Robert Browning. Analysis of Robert Browning's works

Stanza Ten
I told the father all his schemes,
Who were his comrades, what their dreams;
`And now make haste,’ I said, `to pray
`The one spot from his soul away;
`To-night he comes, but not the same
`Will look!’ At night he never came.
The woman tells the father the plans for her lover, his companions, and their multiple goals. The priest then says he must pray to wipe away her lover’s sins. Finally, he says that her lover will return to her tonight, but he will be a different man, changed, as now his sins are gone. But the woman waited, and her lover never returned to her that night. 

Stanza Eleven

Nor next night: on the after-morn,
I went forth with a strength new-born.
The church was empty; something drew
My steps into the street; I knew
It led me to the market-place:
Where, lo, on high, the father’s face!
She waited longer, and the man did not return the next night either. So the morning after the second night, she returned to the church to seek answers about why her lover did not return. But, when she arrives at the church, it is empty. The entire church was gone, devoid of all people. Then she gets a bad feeling and steps into the marketplace by some unknown compulsion. She sees the priest there but is shocked by his appearance. 

Stanza Twelve

That horrible black scaffold dressed,
That stapled block … God sink the rest!
That head strapped back, that blinding vest,
Those knotted hands and naked breast,
Till near one busy hangman pressed,
And, on the neck these arms caressed …
In stanza twelve of ‘The Confessional,’ the woman sees the priest standing next to a man about to get hung. The woman describes the priest and the man and, in her horror, realizes that the man about to be hanged is her lover and the priest has betrayed her trust. The priest deemed the man an enemy of the church, and instead of washing his sins away, they executed him publicly. The woman cannot process the moment, and you feel her shock at the realization of what is happening around her, that she had been tricked and had accidentally killed her lover. 

Stanza Thirteen

No part in aught they hope or fear!
No heaven with them, no hell!—and here,
No earth, not so much space as pens
My body in their worst of dens
But shall bear God and man my cry,
Lies—lies, again—and still, they lie!
The poem brings us back to the present, where the woman is in an unknown prison. We do not see her capture nor the prison’s location, but her words can infer that the church imprisoned her. She yells out that they are liars, that they continue to lie, and that they cannot be trusted as holy men, for they do what is good for them, not what is the holy or just decisions she had been expecting when she initially walked into the church that original time. 
FAQ
What did the lover do to get hanged in ‘The Confessional‘ by Robert Browning?
The reader never finds the exact details of what the lover did or planned to do. However, it is noted that the priest seems to recognize the name when the woman says it, meaning he is somewhat well known, and the word schemes are used by both the woman and the priest, so it can be said that perhaps the man was planning some more devious goals. But, we cannot be sure, as it’s left purposefully vague, perhaps to cement the fact that the priest is the antagonist of this story.
Who is the speaker of ‘The Confessional‘ by Robert Browning?
The speaker is an unnamed woman who is telling her tale of imprisonment. 
What is the “sin” the woman talks about committing in ‘The Confessional?’
The woman had sex out of wedlock, which is considered a sin in the church.
Why was the church empty when the woman returned at the end of ‘The Confessional?’ Was it a fake church? Had it all been planned?
No, the church was real. It was just that all people who were usually at the church were instead at the hanging of the lover. All those same holy people were at the execution. So when the speaker says the church was empty, she means physically, the building was still there.