Is a brother sinful if he subscribes to the internet for his sister, and she then uses it for unlawful things, and is it sufficient to take a pledge from her not to use it in ways that displease Allah for him to be absolved of responsibility?

If there is no certainty or strong presumption that the sister will use the internet for impermissible matters, then there is no harm in allowing her to do so, because the default is to assume good intentions of a Muslim. However, if there is a strong presumption or it is known that she will use it for impermissible matters, then it is not permissible to enable her to do so, otherwise the enabler becomes a partner in sin. And if it later becomes clear that she used it for something impermissible, then there is no sin upon the enabler for what has passed, but it must be prevented from her in the future. And she should be advised kindly and reminded of Allah and repentance, while striving to strengthen her faith and supplicating for her guidance.