Hello Anishgiri,
To your first question about making that parent relative so it's contents can be positioned absolutely, you are doing that right.
Have a look at a
tutorial about positioning that might explain it further.
As for #wrapper expanding in width or showing a scrollbar, I couldn't get either of those things to happen with the code you've posted here.
I did copy/past your code into a new .html document
with a DocType, maybe you are not using one?