Eunuchs in the palace are often beaten by eunuchs?

Yes

It is common for eunuchs to be beaten by boards and beheaded by the whole family. Companions are like tigers, so are eunuchs.

Eunuchs and ladies-in-waiting have one of the lowest positions in the harem, which inevitably leads them to get hit by the board. Even if the master is unhappy, eunuchs and maids will be punished if they make a slight mistake. The most basic punishment is flogging, that is, getting a board on the ass.