If one mistakenly by extreme tiredness falls asleep at 6 pm one night and does not wake up till 10 am the next morning may they make up the asr, maghrib, and isha of the night before and the fajr of that morning

My name is Abdul Rahman, I became a Muslim earlier this year and I have several questions I wish to ask you.

1)  I currently live with my parents, as I am only 19 years old and still in college.  My parents are catholic, but Praise to Allah they are very accepting of my becoming a Muslim.  However, being in america my parents home has many things which make me as a Muslim uncomfortable.  Such as my parents have a dog which lives inside our home, my parents have family photos and other pictures all throughout or home, my parents drink alcohol and have alcohol around the home.  I have been talking to a very good brother from the Masjid I attend who is teaching me and helping to lead me in Islam he says that I should just do my best to keep my room clean and free of these things.  I do this (I am taking down pictures (although I yet to take down pictures of my immediate family as my mother began to cry when I took down pictures of my school friends, etc. and I try not to allow my parent's dog into my room however this upsets my parent's as they say the dog is part of our family).  I have read and heard that the angel's do not enter a home with a dog or pictures I am very concerned about my situation.  I hope that just attempting to keep my room free of pictures and attempting to keep the dog out will be enough to please Almighty Allah (as this is all I can do while I still have to live under my parent's roof).

2)  I am concerned about another issue as well, right after I became Muslim I was performing some of my salaah prayers at work.  I had to use a compass as I was not very good with nothing my North, East, etc. yet.  I was praying at work in a back room that had many metal shelves and computer equiment I believe it missed up compasses reading ability to make a long story short I prayed a few of my early salaah prayers not facing the correct direction.  Should I make these old salaah, I really don't really remember any # maybe 10 or 20 of my early salaah prayers (the good brother from my Masjid said I did not need to as my intention was to prayer towards the direction of Mecca and that Allah forgives little mistakes like this and I should just forget this and pray correctly from now on.  But still I would like your confirmation please.

3) If one mistakenly by extreme tiredness falls asleep at 6 pm one night and does not wake up till 10 am the next morning may they make up the asr, maghrib, and isha of the night before and the fajr of that morning.  Should one in this situation make them up all in a row telling themselves this salaah is last night's asr, this next salaah is last night's maghrib, and so on.