I wouldn't really pry any blooms too hard, so as not to damage them. They should really open on their own.
Here is the culture sheet for Encyclia cordigera, perhaps you might see something in there which is very different from your conditions.
http://www.orchidculture.com/C...
In general, it would help to know where you live and what kind of set up you have.
About the leaves- if they are still attached, I might leave them alone, since the pseudobulbs on Cyms will never grow additional leaves.
