EFT Concepts:

1) Why doesn't the operator

Mathinline
body H^\dagger \tau^a H \tilde{W}_{\mu\nu} B^{\mu\nu}

 interfere with SM

in the cross section calculations for H -> 2 photons?

It has a different parity than the SM operators which! [Pointed out by Nick Kamp]

2) What's the smallest value of 

Mathinline
body \Lambda_{\rm new\ physics}

 consistent with experiments?

In general, it's around 1 TeV. When looking for EFT operators which produce specific effects (e.g. in flavor physics), it can be much higher.