Issues with bleeding Shimano hydraulic brakes

[weisan]

I ran into two issues with bleeding my rear Shimano hydraulic brakes (BR-RS805)

1. I couldn't push fluid into the bleed port from the caliper after loosening the bleed screw. The cup on the shifter is opened. I have no issue doing this on the other caliper in the front following the same steps or procedure.

2. When I squeeze the shifter, it will soften at first then when I retract the lever and squeeze again, it hardens or won't move much.

What could be wrong?