As a prospective second wife, can I ask my future husband for written conditions before the akad nikah?

You can, and writing them down helps both sides understand the promises clearly. Conditions commonly discussed include your own home, monthly maintenance (nafkah), the rota (turn of nights), and whether you will keep working. The Prophet ﷺ said: “The condition that is most rightful for you to fulfil is the condition by which you make lawful the private parts” (Sahih al-Bukhari 2721). Make sure your conditions do not deny the first wife's rights, for example by asking that she be divorced or her turn reduced. Discuss them with your wali, and ask the religious affairs office or a syarie lawyer how to record them so they can be referred to later. See promises before the second akad.