Should those who enter while the Imam is delivering the sermon for the Istisqa prayer pray it after he finishes, or should they sit down? And should it be made up, or should they pray in congregation?

If the Istisqa' (prayer for rain) is missed, it is not to be made up. However, whoever arrives while the Imam is delivering the sermon should pray two rak'ahs as تحية المسجد (greeting to the mosque), then sit down to listen and say 'Ameen' to the Imam's supplication. They should not pray it in congregation.