1. When exporting PDFs, I lose my page names on multiple page projects. In CorelDRAW, the page names are converted into bookmarks. Is there a way to fix that?
Within the PDF Export dialogue box select Advanced Options / Layers and ensure Generate Bookmarks is checked - with Adobe Reader you will see the page thumbnails, but you can select the file symbol to show exported page names. This option is however greyed out for Commercial printing as you might expect. There are lots of custom options too.

2. The second question has to do with the upgrade service. It seems that I have a year's service included with my purchase. (By the way, the backup DVD was purchased as well.) What I wanted to know is, if I switched computers, and did a reinstall from the disc, would I be able to download the updates I had after the year is over without purchasing the additional service?

Yes, correct when you purchase Xara software from Magix, you receive any updates to that software in the following 12 months together with Magix support should you need it. Thereafter, you have the option to renew that update service for a further period of 12 months. Should you choose not to do so, then you will not be able to access any updates or seek support. For example, after update service expiry you can download the last major release e.g. v17.0, but point releases e.g. v17.1 (as I understand) would not be available. The corollary to that is should there be a major update in your active service period, that becomes the fullback release available via your Magix Account product downloads page. There is lots written about the Magix Update Service on this forum (via search), but should you chose not to renew then it is best to download the Online Catalogue before your update service expires. The latter is well documented on this forum too.