It depends on the flower. Some have none, others have very many. Some, like the sunflower appear to have many when you consider only the petals but the number is smaller when you take account of the central seeds.
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yes
Yes it does. As long as it has a symmetry without rotation. If you do the rotation either way it does have symmetry. :)
Flowers display a number of forms of symmetry, reflection, rotational etc. You need to be more specific regarding what type of flower you are asking about.
A trapezoid has no rotational symmetry.
No a Z doesn't have a rotational symmetry