Day Questions

Is it possible to join in the 4th rak'a of the imam after the bowing has already been completed? If so, then how?

Yes, it is possible to join after the last bow by reciting Takbeeratul-Ihram ("Allahu Akbar") and following the imam in prostration until the imam finishes the prayer. The prayer is continued - without counting the prostration with the imam as part of the first rak'a - by standing for his first rak'a without reciting Takbeeratul-Ihram again.

Can I follow a prayer imam if I do not know whether he is Adil?

The prayer behind a person whose Adalah is not established is void.