Can someone explain this process. Will the city hold up (can they) the development at site plan approval if they have wind concerns?
Yes, they can. Wind can be mitigated by architectural treatments, which aren't necessarily addressed at the zoning stage.
Now, they can also be addressed by something that would be (setbacks); orientation of massing, or balconies.
But relatively minor changes in cladding, adding 'fins' or an overhang etc. can also address the issue. Tweaking setbacks, particularly if adding/increasing them, can be done through C of A, or maybe even SPA.
Also, what good is talking to the nearby church about shadowing after the application is approved? Wouldn't these issues typically be addressed prior to approval?
Now that is a good question. Shadowing is a result of height, and massing/floor plate size. Assuming a developer doesn't voluntarily walk back their height permissions.....that only really leaves open the option of shrinking the floor plate, presumably at higher levels to mitigate shadowing.
(I'm slightly over simplifying as sometimes a few cute little moves like a corner rounding can make surprising differences, but I digress)
Suffice to say, mitigating shadowing is much more likely to require revisiting zoning.
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I should add here, that a City refusing to grant SPA can result in an OLT appeal, just like zoning. In which case the OLT is the arbiter of whether the City is being reasonable.
