Is it permissible to pray with a heater (stove) in front of me?
There is no harm in praying with a heater in front of you, as long as you do not intend to venerate the fire or imitate those who worship it. And Allah Knows Best.
Is it permissible for a woman to visit the doctor while in her `Iddah (waiting period)?
It is permissible for her to do that during day time, but it is impermissible for her to leave her house at night except for a sound reason. And Allah Knows Best.
Is it permissible to say: "O Allah, by the status of the saints and the righteous, and our master Muhammad, peace be upon him, grant us the ability to reach Ramadan"?
What is mentiond by the righteous predecessors that they used to say: "O Allah bless us in Shaba'an and Rajab and give us the ability to reach Ramadan." [Shoa'ab Al-Iman/vol.3/pp.375]. And Allah Knows Best.
It is stated in the Noble Quran that pork is forbidden for Muslims. Why is that so?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
To Allah belongs the dominion of the heavens and the earth and He makes certain things allowed for us, while others are declared prohibited. Consequently, He the Almighty wouldn`t make something prohibited unless it is harmful; whether we are made acquainted with the reason or not. Moreover, medical doctors have stated that there are many harms for pork. And Allah The Almighty Knows Best.