What are the characteristics that an suitor must possess for him to be considered among those referred to in the hadith: "If someone whose religion and character you approve comes to you asking for marriage, then marry him. If you do not do so, there will be tribulation on earth and widespread corruption"? And should the suitor be informed of the refusal unless he abandons the sins he commits, or is it better to agree to him and try to change him gently after marriage?

The intent behind "whose religiosity and character are pleasing" is that the suitor should be a righteous Muslim, of good character, upright, performing his obligatory duties, and avoiding major sins. This is a recommendation, not an obligation. There is no sin upon the woman or her guardians for rejecting a suitor, and a woman's marriage to a disobedient person is valid. A woman should choose a righteous husband and consider the totality of his characteristics. There is no harm in making the acceptance of a suitor conditional upon his abandoning some sins or performing some duties.