Is it correct that everything dry is pure even if it has impurity on it?
If something impure becomes dry, it remains impure and is not purified by drying. However, the impurity does not transfer by touching it if the one touching it is also dry. And Allah the Almighty knows best.
Is it permissible to appoint a proxy for the sacrificial offering outside Jordan?
In the name of Allah; all praise is due to Allah, and peace and blessings be upon the Messenger of Allah.
It is permissible to appoint a proxy—whether an individual or a charitable organization—to perform the sacrificial slaughter (Udhiyah) on one’s behalf, even if it is carried out in a country other than that of the donor. This is conditional upon the proxy’s adherence to the established requirements of the Udhiyah, including the animal’s age, its freedom from physical defects, the designated timing of the slaughter, and the proper distribution of the meat.
However, it is preferable for the one offering the sacrifice to perform the slaughter personally, in order to attain the full reward and blessings of the act. And Allah (Exalted be He) knows best.
Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?
All perfect praise be to Allah,The Lord of The Worlds He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah Knows Best.
Who is the one required to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered by the guardian of the newborn — the one upon whom the child's financial maintenance is obligatory — provided he is financially capable of doing so. 'Alī ibn Abī Ṭālib, may Allah be pleased with him, reported: "The Messenger of Allah ﷺ performed the 'aqīqah for al-Ḥasan with one sheep." — Narrated by al-Tirmidhī. And Allah Almighty knows best.