Hello again guys.
With the great advises of howardpc, I was able to find the right settings for my project.
Here is what I have learned, among other things:
1. To select the right tabsheet, set:
CurrentTabSheet.Parent.Activepage := Sender as TTabSheet;
2. Use BorderSpacing and AnchorSide to align the child components of the CurrentTabSheet.
3. For Left, Height and Width of the concerned component, do not use the main form as referencing control but the parent of the component.
4. At maximized main form, before you create the first tabsheet, get Height and Width of the parent PageControl, otherwise the tabsheet will take the parent PageControl with normal sizes as reference. The same is true when you resize the form with already created tabsheets.
For who is interested of working with tabsheets at runtime, please find in attachment the zipped files of the working interface for my project.
Greetings.
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Linux x86_64 GTK2, Lazarus 2.0.10, FPC 3.2.0