When starting odrive you will always see a lot of network activity because odrive will be reaching out to verify that every exposed folder is in sync. From the diagnostic it looks like you have about 6400 folders in scope, locally, so that is a fair bit of checking. During this period you will not see any odrive icon activity. The thinking behind this is that it is just background checking and the user doesn't need to be bothered with it while it is happening, as this can cause confusion when there isn't any apparent transfer or local filesystem activity.
I just ran a test with about 1500 folders in Amazon Drive and the background activity took about 10 minutes to fully finish. During that time activity is heavy, although the payload is fairly low. After that there will be sporadic activity, depending on the number and type of links you have.
odrive is an active syncing engine, and it attempts to give the user an experience that quickly responds to changes. This means its never going to be completely idle for very long. It can also be "heavy" at times. This may be especially true if you are using odrive for more for backup, and less for full, always active sync. (Some more of my thoughts on that: https://forum.odrive.com/t/backup-one-way-sync/1058/11)
We are currently working on optimizing the bandwidth use and background actions, so I expect things to get more lightweight in future releases. Additionally, our forthcoming backup will cater to certain datasets/use cases better than sync. For you mother, if she has metered bandwidth, then this could impact here. If her issue is more just slow speeds, I wouldn't expect this to affect her too much, especially if she has a smaller dataset than you to work with.