Place your files, you'll lose (most of) your editability (and flexibility) and make your ID file bigger if you paste.
If you need to make an edit to your placed ID file, simply alt + double-click it.
Illustrator usually creates PDF compatible files - that's quite normal.
Layers - no.
To expand a little, it is possible to paste even an entire ad as editable paths (you may need to uncheck Prefer PDF When Pasting in the Clipboard Handliing section of the prefs) IF it is simple enough, but your text will be converted to outlines and will not be editable, and when the illustration becomes too complex it will paste as a single PDF object no matter waht you've selected.
For the record, except for a very isolated shape or two that were easier to draw in Illy and then paste into ID that needed to be editable when they got there, I have ALWAYS come to regret having made a decision to paste from Illustrator rather than Place the file. It may take a year or more, but inevitabley I find I need to re-use the object, and then I find I need to make some change and have to edit in multiple places instead of just opening the original and updating the links.
Place the illy file into indesign and as peter says you can alt double click and go back to illy to make any changes, would suggest keeping the illy files as native format and not save them as pdf.
Copy and paste illy files will make your workflow much slower (depending on how many and how complex) but a placed illy file will be much better.
Two ways, Save the illy file as a ai and place that or "save as" into another folder as a pdf and place that you can save the ai to the pdf again if any changes need to be made and indesign will update the link for you.
Save the file as an .ai file. In the second dialog box make sure the box that says Create PDF Compatibile File is checked.