You can fix both of those problems...
1. On the Repository module Settings page, there is a section for security, check the 'Registered Users' checkbox in the Moderator section. If a person is a Moderator, then their uploads will not require moderation. Now, if you want to hide the Moderate button, so only Administrators will see the Moderate button, add a 'Roles' attribute to MODERATEBUTTON token in the header.xml file as follows...
<Object>
<Token>[MODERATEBUTTON]</Token>
<Settings>
<Setting>
<Name>Roles</Name>
<Value>Administrators</Value>
</Setting>
</Settings>
</Object>
This will cause the Moderate button to only be injected if the current user is a member of the Adminstrator role. So, by making those 2 changes, Registered Users will be able to upload items without moderation, but will not be able to moderate any uploads, only Administrator will see the Moderate button. That way if you want to all other users to upload items but have those uploads be moderated by an Administrator, you can do so.
2. Modify the form.xml file for the template you are using, you can set values for RepeatDirection, RepeatColumns and RepeatLayout for the Categories control.
<Object>
<Token>[Categories]</Token>
<Settings>
<Setting>
<Name>Select</Name>
<Value>MULTIPLE</Value>
</Setting>
<Setting>
<Name>RepeatColumns</Name>
<Value>3</Value>
</Setting>
<Setting>
<Name>RepeatDirection</Name>
<Value>Vertical</Value>
</Setting>
<Setting>
<Name>RepeatLayout</Name>
<Value>Flow</Value>
</Setting>
</Settings>
</Object>
The Values for RepeatLayout can be "Table" or "Flow". The values for RepeatDirection can be "Vertical" or "Horizontal". The default value for RepeatColumns is "1" which is why you are seeing the layout you are in your screenshot.
Hope that helps, if you have any problems, just yell :)