1)Even if one is unable to daven in a Shul (due to being ill, or any other halachically acceptable reason), and he cannot easily arrange a minyan to daven in his home, he should at least daven [Shemona Esrei] at the same time that the Shul in his city is davening.
If there are many Shuls in his city, he should daven at the time that the Shul that he usually davens in is davening. Rav Shlomo Zalmen Auerbach Zt"l maintained that one may choose any Shul [in his city] that is davening at that time, and have in mind while davening at the same time that they are davening, to daven along with them and thus be a part of the "Tzibbur".
2)If one is davening Shacharis at home at the same time that the Minyan is davening Musaf (or any other Tefilah, other than the one he is davening) it isn’t considered "davening at the same time as the Tzibbur". (However, if one davens Shacharis with a Minyan in Shul that is davening Musaf it suffices for his obligation to daven at the same time as the Tzibbur, and may even be considered "Tefilah B’Tzibur" according to some Poskim).
If the minyan one usually davens in has the custom to daven Ma’ariv before sunset, and he is davening at home, he should rather wait until after sunset and not daven at the same time as them.
Our holy sages, the Chazal tell us תנא דבי אליהו כל השונה הלכות בכל יום מובטח לו שהוא בן עולם הבא, שנאמר הליכות עולם לו, אל תקרי הליכות אלא הלכות - one who studies [at least two] Halachos daily is assured a portion in Olam Haba-the world to come. (:מגילה כ"ח )
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