Jamaat Salaah and Imaamat

Q: I want to stay home to focus on my studies and quit going outside because whenever I go outside the home, I get distracted. Can I perform my salaah at home rather than in the musjid?

Q: Do I have to makeup for salaah if it was led by a child who is not a mukallaf?

Q: Namaz behind such imam: 

If there's a Barelvi masjid in my area and they say the following before or after azan: "assalatu wassalamu alaika ya rasulullah wa ala alika wa ashabika ya noor Allah" 

Can I pray behind them and if not, should I repeat every prayer behind them?

Q: 

1. If the latecomer joins the Imam in the first or final tashahhud for even a moment, then does the latecomer finish his tashahhud before rising up (for either the third unit, or to complete his missed units)? If the Imam rises quite soon after the latecomer joins him in the first tashahhud, then is it a factor that the latecomer may be behind the Imam? 

2. A latecomer makes the opening takbeer while the Imam is in the first tashahhud. If the Imam begins to rise for the third unit while the latecomer is going down, what does the latecomer do? 

3. A latecomer makes the opening takbeer while the Imam is in his final tashahhud. If the Imam says the first Salam while the latecomer is going down to join him, what does the latecomer do?

Q: Are women allowed to attend the masjid for 5 times daily salaah with congregation? Just like how in the western countries it's done? 

Q: Is it possible for a man to lead in salah his female mahram family members? So can one man and one woman pray in congregation? 

Is the presence of atleast 2 males necessary for congregational salah?

Q: 

1. Will a clean shaven Hafiz be termed as a fasiq in Shari'ah? 

2. Will his Shahadat be accepted? 

3. Can he lead Taraweeh Salah in his own house with people behind? 

4. Can he be appointed to assist with administrative and running of finances in a Masjid?