Yes. MOLE has a fully documented and supported API. You can find standard ArcObjects developer help and developer samples in Java, C++, and DotNet included with the MOLE installation.
MOLE can use any supported ArcGIS vector format data that meets a few minor schema requirements (like a Symbol ID code field). There is a geoprocessing tool included with MOLE that will add the required fields automatically.
Yes. MOLE works in ArcGlobe, an application within ArcGIS 3D Analyst. Force Elements are positioned on callout lines and billboarded (always facing the viewer) and Tactical Graphics are extruded. The user has control over how this appears in ArcGlobe.