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Now there are some small details of this whole calculation that I'm confused about.

I followed all the way through to (2.25), but here I feel a bit weird.

Isn't he trying to expand Φ(p)=(constant factor)(a+a* ) and plugging this back into the fourier expression above (2.21)? However (2.27) directly contradicts this, instead he is taking Φ(p)=(constant factor)(a(p)+a*(-p) )

I understand that this is required to make the operator hermitian, but how is this formally justified step-by-step?

(Here I use * as a poor man's dagger)