What information is accessible through iCloud? Can the administrator on my home PC access these files?

Assuming your talking about Windows and the other user has administrator rights:

There are tools that may allow the Windows administrator account (which has access to all files on the computer) to view locally stored backups and extract them. This will only be possible if the data is actually on this computer, and not encrypted.

If you are sure that is not the case –because you only backup to iCloud– this person will need your Apple ID and password to access your iCloud data. This information may be stored in your session (recorded by Chrome for instance) but it is encrypted with a key associated with your Windows password, so not accessible to the administrator.

If the administrator changed or knew your Windows user password he could have accessed your session and pretty much all of your data. You will notice on the first case because he will have asked you to recreate it, or use a new one. It does not seem possible for the administrator to see your stored password, only to reset it.

Finally, someone could have installed a keylogger or some other form of monitoring on this computer, and all the information entered could be retrieved.

On the other hand iMessage is encrypted end to end according to Apple and others, but probably available to Apple or someone with access to Apple's servers (see this answer on Information Security SE). Sniffing your traffic on the local network and extracting iMessage from there does not seem to be a feasible attack vector.

To keep this from happening:

• Change your Apple ID password. Check your recovery email and security answers to see if it any of them have been changed.

If you use the PC to access iCloud

• Change your Windows user password.
• Don't store passwords on your Windows user session (browsers mainly). At least not your iCloud password or the passwords of the email accounts associated to it.
• If you suspect a keylogger or other monitoring tools, stop entering information associated to iCloud on this computer.