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Why VS2010 puts this kind of information (function names) in Release mode to executable?
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Can i get rid of all unused data/segments in exe file, re-link it, re-build it etc. with help of some third-party software that would “analyze” the existing .exe and rebuild it?
- Can i compress .exe file to shrink its size by adding some decompressing-on-start binary code to it?

As a matter of fact, it is not really VStudio that puts these details but the Qt libraries that your project statically consumes. Qt is well known to be “generous” as far as the size of libraries is concerned.
Yes, having these details helps to have an idea about the features of your software. (e.g. using Qt).
UPX is well-known and very performant as far as the compression and portability is concerned. But don’t forget that UPX is a compression (and decompression) mechanism and NOT an encryption mechanism. To hide some exports table, etc…you might use a real compression and encryption package like VMProtect