The /activities API provides two ways of managing paging - by default the page size is 25 as you've noticed:
1. You can use the lastId parameter to fetch 25 activities after the last activity id you previously received.
2. You could use the Range: items=N-M header for custom paging, but based on a quick test this does not work as expected - I filed a bug for this.
The TC .NET SDK does provide support for fetching activities using projectClient.Activities.GetAllAsync() where the lastId parameter can be set via the parameters dictionary.