Is it obligatory to inform a suitor about a crooked nose if it is not apparent? And is it permissible to reject a suitor who prays at home and does not pray in the mosque, out of a desire for a husband committed to praying in the mosque?

You are not obligated to disclose the tilt of your nose to the suitor, as it is not among the defects that necessitate disclosure or establish the right to annul the marriage. It is permissible for the suitor to look at the woman he intends to marry, or to send someone to describe her to him. It is preferable to choose a suitor who is observant of congregational prayers, but the main consideration is that the suitor is, in general, pleasing in his religious commitment and character.