I agree with mrbungalow on the first one. Not only does the whole plant look identical to my Ice Cream banana, it has black pepper markings like my Ice Cream banana does. Look where the leaf meets the pseudostem.
The sucker shows the dark midrib like a sucker on mine, too.
The plant and pup both have a striking resemblence to Ice Cream.
When it flowers you'll have a better idea. It's only a matter of time