I have been able to add a web part, thank to this post, using code like:
limitedWebPartManager.ImportWebPart(webPartSchemaXml)
However now I'm not able to remove the Web Part anymore by Editing the Page, because the Web Part is not visible in Edit mode (incidentally I don't know why).
So I'm trying to Remove the Web Part programatically, but LimitedWebPartManager doesn't offer a method like RemoveWebPart
.