How is the hydrazone formed in the Wolff-Kishner reduction?
Wolff–Kishner reduction is the method for the reduction of aldehydes and ketones to corresponding alkanes. First, the carbonyl compound condenses with hydrazine to form the corresponding hydrazone. The resulting hydrazone is treated with base to induce the reduction of the $\mathrm{sp^2}$-carbon to $\mathrm{sp^3}$-$\ce{CH2}$, and the oxidation of the hydrazine to gaseous nitrogen in the process to yield the corresponding alkane:

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The following is the accepted mechanism of the reduction:

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How does the formation of the hydrazone occur in basic conditions?

The formation of the hydrazone can be done in either acidic or basic conditions (recall imine formation of aldehydes and ketones with primary amine and 2,4-dinitrophenylhydrazone formation of  them with 2,4-dinitrophenylhydrazine). And, yes, as Wikipedia mentioned, sometimes it is advantageous to use a pre-formed hydrazone as substrate for the reduction. Yet, remember, Wolff–Kishner reduction is better suited for substrates with acid sensitive groups. Therefore, use of acid catalyst to pre-form hydrazone for the reduction is meaningless in that situation.