I see that for the paid version (which I do not have), it says you can download maps for offline use. How does that work? I'm going to a park with no internet access. If I download the map, will I still be able to use real-time navigation (assuming my gps on my phone works), or is it just like having a pdf of the map available on my phone?
Yes, you can then also plan routes and/or navigate offline. The routing data is also downloaded and is then available offline.
However, you need to check which router you have selected in the navigation settings. Normally, Online LoRouter is selected there. You should then select LoRouter Offline.
The routing data is downloaded with new maps. But you should update it from time to time. When offline, you can choose how often. I don't remember what the default setting is here.