Yes, the .NET version of the application pools should be the same as the .NET version of the binaries.
The web request does not reach our application and this is why you see an error from the web server not from our classes. Your IIS server cannot process the request and this is a server side issue. I do not see what else could cause this issue when the error clearly states that your IIS server tries to serve a page by its static handler. You have a mapping for that content to something other than StaticFile, but that handler mapping does not apply for the current pipeline mode (integrated/classic), bitness (32/64 bits) or even asp.net version
Your account shows that you have two downloads
Sitefinity_3_7_2136_standard_trial_NET20.exe - this is for .NET 2.0
Sitefinity_3_7_2136_standard_trial.exe - this is for .NET 3.5
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