Yes. In addition to configuring the primary external editor, you can set up additional configurations for the same editor, or a different one, in the Additional External Editor section. When you save additional configurations as a preset, they appear as a menu item in Lightroom’s Photo > Edit In menu.
Photoshop’s Camera Raw plug-in does the rendering when you pass a raw file from Lightroom to Photoshop by pressing Ctrl+E/Command+E.
Passing a raw file from Lightroom to Photoshop and saving it in Photoshop generates a PSD file. That said, if you picked TIFF in Lightroom’s External Editing preferences, you get a TIFF instead.
No. When you reopen a PSD that you’ve edited in Lightroom using the Edit Original option in the Edit Photo dialog, the last round of adjustments you made in Lightroom are not visible in Photoshop due to the special flattened layer that Photoshop includes in the document. Therefore, you’ll have to redo those adjustments once the edited PSD returns to Lightroom.
Yes, but only for raw files. If you create snapshots for a raw file and then send it to Photoshop as a Smart Object, you can double-click the Smart Object in Photoshop to open the Camera Raw plug-in. When it opens, click the Snapshots panel, and you’ll see all the snapshots it contains.