This question belongs to Products. Please move it there, and you will get more answers
And no, you cannot have nested containers, not even 2 containers in 1 templates. Read this Email editor 2.0 is leaving room for a v2.1
Usually, lines appear on tables on some older email clients because you have forgotten to add cellpadding="0" cellspacing="0" border="0" attributes to the table as well as proper CSS to also remove any border.
You can also set the background color of your container with 1 variable.