How are the missed rak'ahs made up for one who joins the congregational prayer in the third rak'ah or later, and should one sit for the first tashahhud, and does this method apply to all obligatory prayers?

What you catch of the prayer with the Imam is the beginning of your prayer, and what you pray after the Imam departs is its end. So, if you catch the Imam in the second rak'ah, you stand up after he departs for the third rak'ah, which is the third for you, and you do not sit except in the last rak'ah. Your sitting with the Imam in the final tashahhud (definition) suffices for the middle tashahhud. If you miss three rak'ahs in a four-rak'ah prayer, you sit for tashahhud three times. This is the more correct opinion.