Hello Yuhui,

>> In PIM BIDIR, it is ok to forward the mcast traffic out of the interface where it was received, is that right?

this is not needed so it shouldn't happen

>> Will there be a case that the elected DF does not get any mcast traffic from the sender/source while the non DF router does?

you need to think of DF in regards of two aspects:

DF towards RP = router with best path to RP

DF  for a multicast source = router with best path to the source

so the above can happen traffic can arrive in the lan segment and then if it can be propagated towards RP by a different device.

>> Will there be a case that there will be a split view over the DF over the LAN?

Consider DF a relative concept in the lan segment as explained above.

Hope to help

Giuseppe