How should one deal with a brother who is 100% mentally disabled and has lust and desire for women? Is it permissible to give him medication that would suppress his desires, so that he becomes one of "those who are free of need among men"?

It is not permissible to give your brother medicine to curb his sexual desire, due to the harm and injury it entails, and because of the Prophet's (peace be upon him) saying: "There should be neither harming nor reciprocating harm." It is advisable to seek a way to marry him off, because it is permissible for a guardian to marry off a madman, an imbecile, or those in a similar category, if there is a benefit in doing so. Indeed, some scholars explicitly stated the obligation of marrying him off.