What is the ruling on disavowing and shunning people of innovation, even if they are family members, and what is the ruling on praying and performing ablution according to their madhhab? Is it permissible to delay prayer or miss some obligatory prayers due to the inability to outwardly disavow this madhhab to family members during studies?

As for the people of innovation (Ahl al-Bid'ah), it is obligatory to disavow their innovations, and boycotting them is subject to what is in the best interest. As for ablution (wudu') and prayer (salat), a Muslim must perform ablution and pray as Allah has commanded, without neglecting the duties of purity and prayer. One should openly proclaim the true madhhab (school of thought) and invite people to it, as long as no harm is feared. If there is a fear of someone becoming aware of one's prayer, one can pray discreetly, or be permitted to combine two prayers if discreet prayer is not possible, as fear is among the excuses that permit combining prayers. It is not permissible to delay prayer beyond its prescribed time without an excuse. If one is unable to perform any part of the prayer due to fear of harm, that part is waived.