Jamaat Salaah and Imaamat

Not joining the jamaat Salaah

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?

Performing fajr Salaah at home if one fears missing the Salaah

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.