I don't believe Presenter offers that level of control. For this, you would need to edit the video using a different application. Premiere Elements, Premiere Pro, TechSmith Camtasia, etc.
Yes, you will need an actual video editing tool to do that. You could then bring the video back into Presenter as well. When using APVE, it would be best to plan on using dummy information or a version of your tool that won't contain sensitive information. This can eliminate your need to obscure portions of the capture.
As to the text, I suppose you could add text in PPT and layer it on top of the video, but that feels like a bit of a hack. There is the ability to have text in the name and title fields at the bottom of the captured video, but I suspect that isn't exactly what you are looking for.