Yes. The extension allows for complete customization by writing macros in Visual Basic for Applications (included with ArcGIS for Desktop) or creating extensions for ArcGIS for Desktop developed in standard development environments (Visual Basic, C++, Delphi, etc.).
Data can be updated as close to real time as your system allows. Data rates depend on the communication links to the data applications you are using, server speeds, and network speeds. The display rate on the screen is limited to one refresh per second; however, each refresh may update multiple objects.
Tracking Analyst supports all ArcGIS vector formats (points, lines, and polygons). However, all data must have a Time & Date field in it. Usually this is in the format MM/DD/YYYY HH:MM:SS; however, numerous date formats are supported.
If some of the features being imported do not have a valid format for the Date field, then the feature in question is not included in your new Temporal Feature Layer. Make sure that the date field is properly formatted for the missing features.