I found something else: As it seems, the table is wrapped in a
<pre> HTML tag, which basically influences the styling a lot, as this is intended for other purposes.
<pre> is wrapped around the table Shortcode already, from copy/pasting.
Please go to the "Edit" screen of the page (where you entered the Shortcode), and switch from "Visual" to "HTML" editing (in the upper right-hand corner of the editor textfield) there.
You now probably see something like this:
<pre><span style="font-family: verdana, geneva; font-size: medium;">[table id=4 /]</span></pre>
Please remove the surrounding HTML tags, so that this line only is the Shortcode
[table id=4 /]
After that, the table should be visible as a table again (with all columns), and some word wrapping. We can then continue with changing the column widths.