Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
What is the ruling on ablution if vaginal discharge is expelled, and is it impure?
If these discharges exit from the external genitalia (apparent part of the vagina), they are not impure and do not invalidate ablution. If they exit from the internal part, they are impure and do invalidate ablution. If it is uncertain whether they are from the internal or external part, they are not impure and do not invalidate ablution.
The apparent part is what becomes visible when sitting, and what the husband's penis reaches during intercourse is considered part of the apparent. The internal part is what is beyond that. And Allah the Almighty knows best.
How does the person praying perform the prostration (Sujud)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is an act of Sunnah for the person praying to descend for prostration (Sujud) by placing their knees first, then placing their hands on the ground, and then placing their nose and forehead simultaneously. It is obligatory that the toes of the feet be on the ground, directed towards the Qibla. And Allah the Exalted knows best.
How can I love the prayer (Salah) and start praying?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Love for the prayer (Salah) comes when you realize that this world is fleeting and the Hereafter is everlasting. Your prayer is the righteous deed that will comfort you in your grave and be your salvation before Allah in the Hereafter. Do you not wish to attain tranquility in this life and Paradise in the next? Reflect upon your state and do not delay, for life does not wait. We ask Allah to grant us and you steadfastness (Thabat).