Is it permissible to make ablution without answering the call of nature after waking up?
Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najaasah (impurity), thus if there is no Najaasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature. However, prayer is invalidated if there is Najaasah on the anus ,or the front opening, so it (Najaasah) must be removed for the prayer to become valid, and not the ablution.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
Is it permissible for an elderly person, a pregnant woman, or someone with a chronic illness to pay fidyah before Ramadan begins?
It is not permissible for an elderly person, a pregnant woman, or someone with a chronic illness to pay fidyah before Ramadan begins.
Additionally, it is not allowed to pay fidyah for more than one day in advance, because fidyah is a substitute for fasting, and fasting is not yet obligatory at that time.
However, it is permissible to pay fidyah for a single day in advance, by analogy with paying zakat up to one year in advance.
Is it permissible to combine Zuhr and Asr prayers for being occupied with a wedding ceremony?
No, it isn`t permissible to combine Zuhr and Asr, or Maghrib and Isha because of being busy with a wedding since the exemption for combining prayers is based on lawful excuses, and this isn`t one of them. And Allah Knows Best.