Behavior of saving value of property in DFM is controlled by Storage Specifiers:
1. It's Storage Specifier "default" value. So, if your property defined like:
property MyProperty: boolean read FMyProperty write FMyProperty default true;
and on moment when you save form into DFM value of your property MyProperty is true, it's will be not written into DFM file.
2. It's Storage Specifier "stored". by default it's TRUE, but you can write constant FALSE or use Boolean function to change behavior for specified situations.
More details here
So, for your case, you can try to redeclare published properties in class TBaseForm with correct (for your opinion) Storage Specifiers.
About changes in DoubleBuffering and RemoteDesktop in new versions of Delphi you can read here
About StyleElements: it's used only on case when you use VCL styles, so if you don't plan to use it - you can just ignore this properties.
P.S. If you want to know which parts of sources IDE use in debug mode, you can debug one Delphi instance from another. Just write some BPL, intall it into IDE, got o Run->Parameters->Debugger->Host Application and set it into "C:\Program Files (x86)\Embarcadero\Studio\23.0\bin\bds.exe", then you can run Delphi with debugging, put breakpoints and see which methods does it use and why save some params.
I think you need to check some TWinControl.IsDoubleBufferedStored method, TWriter and TReader classes, etc.