Signing in through a home computer to work through Citrix

It's remote access and not part of your home network. You can access your local files via citrix but you do have to give it deliberate permission. Based on what I know about it, it seems pretty unlikely to cause an unintentional infection. Network admins here will be able to answer better than I can, though, as I'm just an end user.

If your citrix configuration allows you to map local drives to your remote session, then yes you can fahk your company over and put malware on the network.