No, not exactly, although they are related. Recurrent merely means that something happens over and again. Frequent takes recurrent and adds a relative time span: something happens often again and again.
Often, common, and repeated are all synonyms of frequent.
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periodic, alternate, irregular, seasonal, recurrent
often
Either. If it is non-terminating but recurrent (after some point) it is rational. If it is non-terminating AND non-recurrent then it is irrational.
A synonym for varied is diverse.
A synonym for temper is temperament.