Is it permissible to delay the ritual purification (ghusl) from major impurity (janabah) until after dawn?

Yes, it is permissible to delay ghusl from janabah until after dawn, as purity from janabah is not a condition for the validity of fasting. However, one must perform ghusl in time to pray Fajr within its designated time.

What should a person who was favored from Allah with a newborn, but couldn`t afford an Aqeeqah, do?

Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) is a desirable Sunnah for the financially able since Allah, The Exalted, charges not a soul beyond its capacity. Therefore, if the father couldn`t afford the Aqeeqah before the end of his wife`s confinement, then it isn`t due on him, and if he was able to afford it later on, then it is permissible, but if he didn`t until the child reached puberty, the latter can offer the Aqeeqah himself.

What should a person who doubted having missed a pillar of prayer do?

All praise be to Allah, The Lord of The Worlds.                                                                                                                                                                              The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah Knows Best.

Is it permissible for an elderly person, a pregnant woman, or someone with a chronic illness to pay fidyah before Ramadan begins?