Assuming you are using the Mail app, the spam/junk folder dose not push (or get fetched).
Only the Inbox gets fetched or pushed (depending on your setup). Most other folders will wait until you open them to actually load the email. Trash, Drafts and Sent may be an exception, depending on account type and settings. If you have not opened Mail in a while you'll notice that that the signal icon goes into it's spinning mode (showing that stuff is being downloaded) when accessing your other folders. Nothing is displayed at first. Even then it will only load the first so many. If you scroll down you'll see that there is an option to load more; assuming there are more. How many get displayed depends on your settings in Settings > Mail, Contacts, Calendars; the Mail section.
These extra folders do not get permanent space on the iPad. They are deleted when the Mail app is removed from RAM, either manually or over time as the iPad closes apps automatically.
As far as deleting on the other machine. Both the Exchange and IMAP (default) GMail setup delete email off of the server when they are deleted from the iPad. If this is not showing in Outlook on the PC, it is probably because it is using local folders instead of staying synced with the server. Check your settings in Outlook to change this behavior.
That is all I can think of.
P.S. It is possible to set GMail up as POP3 account, which does not sync with folders on the server. However this is not something you would have been able to do by accident. It requires that you adjust setting on GMail and go through a non-standard mail setup on the iPad.
All GMail access methods that do no go through the Mail app are kept in synch with the servers. Even more so than the Mail app, which is why I haven't mentioned them till now.
