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Hidden elements are grayed out in the tree. Please feel free to provide a more detailed explanation of how do you think this needs to be done. Thank you.
You can create groups using Scene->Create->Group, then you may drag shapes there using the scene tree panel.
Do the right click in the scene tree, then click "Hide selection" to hide the object.
Some images would really help.
Could you contact support with more details about the issue? Origami tries to save images at 300dpi, so the quality should be enough for most cases.