Context Free language, the language empty string (lambda)

Which context free language corresponds to the language empty string
(lambda):

S-->aS
S-->empty string

or
S-->aS

or
S-->empty string

or all of the above. Can you explain if possible, trying to
understand the concept.

Is the following grammar ambigious:

S-->BA|bbA
A-->Aa|a
B-->b

My answer is yes it is ambigious, can you correct me if that is
incorrect and also some explanation to understand the concept...

Thanks
Kind Regards

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