My Encyclia cordigera is actively in bloom however I notice the last 3 petals always get stuck together. So I try to help and pry them apart carefully. Is this common for this type of orchid or is there something else I should be doing for it.

It has been a very windy day here the whole day and when I arrived home, saw that my sedum pot landed on my mini-cymbidium so some parts of the leaves are partially torn from the pseudobulb, should I just removed the leaves altogether? I just feel bad, it takes the pseudobulbs a great while before it produces any new leaf at all

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.

Thanks Ursula for the E. cordigera culture sheet..hmm looks like the temp and humidity..so I will just ignore and let her be, maybe she will do it her own way,I might just be making it too hasty for her At least it is managing to open the buds. I am in the Central Valley area in California, so cool dry winters inland and this year our winter has been much drier, though having a late season winter rain. I grow all my orchids indoors except for the mini-cymbidium. I only bring the mini-cym indoors when it is in bloom, and for this year it has finished her stint.

Yeah, the mini-cymbidium leaves are still partially attached...just looks ugly looking splattered..oh well, live and learn again!

Regarding the Cymbidium - you know, Orchids in nature really don't look as perfect either! They get nibbled on, wind-torn, you name it!

So perhaps your humidity might be a bit on the low side in your area, but as long as the buds do open, who is to argue, right?