Importance of Salaah with jamaat

Q: In the month of Ramadhaan, there are many jamaats for Taraaweeh salaah in our area. Taraaweeh salaah is performed in homes, garages, factories, etc.

Certain people do not perform the Esha salaah in the musjid, but rather perform it at the venue where they perform the taraaweeh salaah. As soon as the time of Esha enters, they perform their Esha salaah and then commence their Taraaweeh salaah. In our area, the musjid is close to the venues of these taraaweeh jamaats.

Is it correct for the people to perform their Esha salaah in the taraaweeh venues or should they perform their Esha Salaah in the Musjid and thereafter proceed to their taraaweeh venues?

Q: I missed my esha jamat just because my parents wanted to go somewhere? For their happiness I missed it. However when I reached there, I went to masjid and prayed alone namaz. Am I sinful?

Q: Is it permissible for me to perform the zuhr salah late at home just during the winter, rather than having to pray every single day at school during the winter?

Q: If azaan has been given for salaah, so it is compulsory to make jamaat?

Q: I know there is more reward for Salaah prayed in congregation for men, please provide me with Hadith to support this fact.

Q: This weekend I was out musafir for a few days with a few friends. We came to a masjid to perform salaah. Two friends we finished making wuduh and the third was still making wuduh so the two of us decided to start our farad thinking the 3rd brother will join us. Our first rakat was almost finished when the third brother finished his wudu. The brother didn't join us but performed his salah on his own. When asked why he didn't join us he said because we didn't wait for him. Is this brother sinful for doing that?

Q: For whatever reason which Allah (Ta'ala) knows best I woke up for fajr salaah a bit later than usuall i.e. within permissible time but not enough to make it to the masjid as I felt I could miss the Jamaah and fall within an impermissible tome. I commenced with salaah and performed a short but not hesty salaah with Jamaah at home. I had completed salaah and tasbih* and dua by 04:35am- 20/12/2015-durban. Latest Jamaat commencment time in locality is at 04:25 (Masjid is Al-Hilal)- did my salaah fall within the permissible time and was my decision to perform salaah at home with jamaat at home valid on grounds that I could have missed salaah and permissible time completely had I driven to the masjid. Note that we follow the Shafi'i Madhab so the duration of salaah included dua e qunoot which was incumbent on me as the imam leading salaah.

Q: I pick up my neighbour for salaah every day. There are times when he is late and I leave him due to my missing the Takbeer-e-ula, which I do not like to miss. Should I miss the Takbeer-e-ula and rather wait for him?

Q: Is is okay for men to pray at home?

Q: Is prayer in musjid obligatory? There is a hadeeth which says something like prayer not being accepted if you hear the azaan and don't go to the musjid. Also there is a hadeeth of a blind man and he wasn't given concession to pray at home if he heard the azaan. Also there is another hadeeth about the prophet (Sallallahu Alayhi Wasallam) wanting to burn the houses of those who don't pray in the musjid. Yet I heard zakir naik say most scholars say it is sunnah muakkada (maybe he meant if we don't hear azaan). Also if prayer is obligatory in the musjid if you hear the azaan, how should this be understood in modern times? Like literally if we hear it? What if someone lives right next to the musjid in a western country but they don't give the azaan through the external speakers of the musjid so the sound of the azaan can just be heard inside, where as in some muslim countries the azaan can be heard from a distance of even 500 meters because of the speakers. Or should we consider how far the sound would travel if done in an open area (desert) and give the azaan without speakers and see how many meters it would travel? Another thing to keep in mind would be thick infrastructure and noise also plays a role on how far the azaan would travel these days. Jazak Allah Khair. Please explain if there has been some ignorance present in my question pertaining to context of Ahadeeth. This is so important as not praying woukd be kufr and if our prayers aren't being in the masjid they might not be accepted. Also what about congregation prayer. Does that suffice? If he hears the azaan but prays in congregation somewhere else? Please provide evidence from Quran and Sunnah.