Should missed Takbirs, or some of them, be made up? And how does one who joins the prayer late catch up with the Imam?

The latecomer joins the Imam in the funeral prayer at whatever point he catches it, based on the Prophet's ﷺ saying: "Whatever you catch, pray, and whatever you miss, complete." If the Imam says the taslim (definition), the latecomer completes what he missed, provided the bier has not yet been lifted. However, if he fears that it will be lifted, he has the choice between completing the prayer or continuing with the takbirs and taslim along with the Imam.