Is it permissible to marry after the husband has been accused of mental illness, and the wife has assented to this misfortune? And is the one who marries sinful if he has a pending divorce case in the courts?

Proving soundness of mind and good conduct does not require a doctor's certificate; what matters is what people observe. If the accusation from your wife's family stems from your actions, then you must address yourself. However, if their accusation is baseless, then advise them and explain to them the sinfulness of such an act. If they do not desist, then sever your relationship with them to prevent them from corrupting your wife. Regarding a second marriage, take your time and avoid letting revenge be its motive, as this could harm the second wife. If the situation with your first wife and her family does not improve, then marry another woman, whether with or without divorcing the first, with a good intention and the aim of reconciliation. Allah Almighty says: (If they desire reconciliation, Allah will cause agreement between them. Indeed, Allah is ever Knowing and Acquainted.) (An-Nisa: 35). Fear Allah and do not let this matter lead to injustice or to reminding her of something she has apologized for.