FYI: The 'FlatPattern' object in a sheet metal part is actually its own different ComponentDefinition, and is actually derived from the ComponentDefinition Class, but with some of its own unique methods/properties, with its own set of Parameters, Features, Sketches, Body, etc. Those Parameters that you create within the FlatPattern.Parameters are not accessible from the parent PartDocument.ComponentDefinition.Parameters, and some of the other properties of the FlatPattern are a similar situation.
If you need to assign a name to pretty much any type of object within Inventor, so you can find it again later, all you need to do is use that object's 'AttributeSets' property, because almost everything has that property. That is what the built-in iLogic 'NamedEntities' Interface system uses, but that system only works in the normal or sheet metal Part environment right now, not in an assembly, and not in FlatPattern editing mode. You can somewhat easily create your own very similar system of identifying things using different names for the AttributeSet and/or Attribute that you place on the objects, without using that iLogic NamedEntities Interface. But if you do go the non-standard way, you would generally have to do some things the harder/longer way on the drawing side, because some of those popular iLogic shortcut snippets may not automatically recognize the entity names. You would have to use the alternative API code process instead (Document.AttributeManager and its tools) for finding the named objects according to your own naming conventions. That type of identification system dates back at least a decade, long before the iLogic NamedEntities system or its associated user interface tools were introduced (back around 2019 version). As you mentioned though, you would have to apply those names to the entities retrieved from the FlatPattern.Body and its associated geometries to be able to identify those in the flat pattern view in a drawing by code. There is almost always more than one way to do things in Inventor.
As for including that sketch from within the FlatPattern into the DrawingView of the flat pattern. That is a tough one. You can definately get a reference to that sketch by code, but the DrawingView.SetIncludeStatus method seems to throw an error when you try to use that for this purpose. I had originally attempted to do this by using the actual command for it, but that was not working as planned either. The command name is "DrawingGetModelSketchesCtxCmd". I attempted to get the BrowserNode of either the view or the model or the flat pattern under the view in the Document.SelectSet, then execute that command, but that was not working for me either, interestingly enough. Good luck with that.
Edit: Sorry, I did not see page 2 of this forum post before posting this response.
Wesley Crihfield

(Not an Autodesk Employee)