I am the main prize in team sports and sometimes a wife, what am I?

I am a tough cut of meat from the lower breast, But give me some time, and I’ll beat all the rest. I love a good rub of salt and of spice, And a low, smoky bath makes me taste extra nice. You must cook me for hours don't rush or be quick, Or I'll turn out as tough as a hickory stick. But stay patient and slow, let the smoke do its part, And I’ll melt in your mouth like a work of BBQ art.

Has stalls, but no horses to feed Buyers browse to find what they need One little piggy went here Wall Street calls it a bull or a bear

Many starved looking for me. I’m an Irish delicacy.

I hang in doorways, yet I never knock. I'm kissed for, not with; a living paradox. Green when the world goes bare, I cling to height, A parasite that somehow feels like light. What am I?