I draw a shape, save it in AI and want to use it in another files as editable template. But when I place this AI into a new file, the shape is shown as an image not a vector. So how to place a vector AI into a new AI file?
You should consider making those shapes into Symbols.
Open the symbol Panel (Window → Symbols or Shift+Ctrl+F11)
To add a symbol, you just select drag your entire shape(s) into the panel.
From there you can create a pack of symbols. To export your pack of symbols click on the menu → Save Symbol Library and you can choose to save it as an
.ai file containing your predefined symbols.
To then reopen that pack just choose the library form the subpack of User Defined
Symbols also help reduce your file size and increase performance of Illustrator - especially when working with a lot of paths, here's a real example.
You can't link to other AI files and have the contents editable via the Link. You need to edit the original AI file if you want the link content to change and retain the link.
However, after placing an AI file you can then embed the link and the art will be fully editable. But, it will also no longer be linked to the original file. Embedding breaks the link and merely copies the contents to the active document.