Concept...Electricity

Q:Is the resistance of an appliance always the same?
(same temp.same shape.same length.same material)

Your question is too vague.
It can only be said that under the same operating conditions, the resistance of a particular appliance would remain unchanged.
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Q: Is the power given out by a cell always the same?
(assume that the voltage given out is always the same)
No. The power delivered by a cell depends on the demand, i.e. the current drawn from the cell. (Power = voltage x current)