Is there a banking mode in Emsisoft Internet Security (as seen here: http://www.emsisoft.com/en/software/internetsecurity/ under Protection tab)?
If yes, where can I find it?
I think this is the answer for your first question: Yes, if you are a current owner of Emsisoft Internet Security Pack (EAM&OA) you should go to the Emsisoft Licence Center and there you can merge your two registered linences (1 of EAM & 1 of OA) into a new EIS licence.