YOu should not use Copy & Paste in such cases.
Save the files, in Illustrator as AI or PDF/X-4, in Photoshop as PSD or PDF.
In InDesign, Photoshop, Illustrator you should always import any file via File > Place…
Actually in indesign if you copy and paste from illustrator you have ability to change colours etc of the individual vectors which is incredibly useful and can then be put into the library or saved as a snippet for others without illustrator, by doing this you are not risking any placed file changes from other documents (for those of us to bone idle to create a proper links database).
I concede however I may have confused myself there, I think you have to change any text to outlines before the copy and paste.
Still a pain with photoshop though, that behaviour has changed from the past where you could determine the size when opening
Never make outlines of tet as you loose hinting.
I once thought that being able to edit Illustrator vector data in ID was a good idea and pasted some art into a series of files. It came back to bite me a year later when the client wanted some changes and I had to edit every single file instead of updating a simple link. It doesn't ake any longer to edit the file in Illustrator than in ID, but it gives you a lot more flexibility.
I am finding it increasingly difficult to copy and paste from illustrator to indesign.
The AI and ID preferences affect how Illustrator items paste into InDesign.
If you want editable vectors set your Illustrator File Handling & Clipboard preference to Preserve Paths:
In ID make sure you uncheck Prefer PDF When Pasting in your Clipboard Handling preference:
You don't have to convert text to outlines, but it comes into ID as EPSText and is not editable.