8 bit vs 16 bit editing in Photoshop - Not sure I'm doing it right...

There is no benefit to changing to 16-bit after editing.

But you can go back to the raw file (in Camera Raw), and open a new copy in 16-bit in Photoshop.

Click the text center bottom of the Camera Raw window to open the Workflow options, and make sure Depth is set to 16-bit.

This setting should stick unless you change it.

Editing should always be done in 16-bit, which gives you editing headroom, and prevents damage to the image.

See https://www.photoshopessentials.com/essentials/16-bit/ for an in-depth discussion.

If you didn't see any difference on your monitor, try viewing the image at 100%, which you should always do to evaluate image quality.

In order:

• After editing? No; only if you intend to apply any further edits to the image would you benefit. Otherwise, don't bother.
• Sure; you gain the benefits---particularly color/grayscale edits---while in 16-bit; I should note: Some filters only work in 8-bit. (insert sad face here)
• Once you use the New dialog, its settings should stick. The option to choose color depth (I believe you can make an action too if you don't feel like going into New every time):

(Before anyone comes at me with, "WhY ARen'T yOU uSInG DarK MODe, brUH???," know that I'm not partial to going blind.)

If you are plamning to do more editing and processing to smooth area using filters the use gradients 16 bit color may help in the smooting processing.  Converting to 16 nit color is not going to gain colors the you lostt  by  converting  Raw to  8bit rather than 16 bit color.  Most Ptinters are 8bit color devices  so you print file only needs to be 8 bit color. Most display and display adapters are 8bit color devives. While my nvidil quadro  and device driver support 30bit bolor I can not use that 30bit color setting I do not have  a High end wide gamit display.  So I user 8bit color depth. 24bit color not 30 bit color.  I do onvert camera RAW images to ProPhotoRGB 16bit color for editing images.

1. No, not unless you end up pasting high bit data into that original, then you'd convert. 

2. Editing in high bit has advantages as discussed here:

http://digitaldog.net/files/TheHighBitdepthDebate.pdf

3. Yes, you can create new documents to be in high bit (what Photoshop calls 16-bit) but if you're working with scans or camera originals, it has to come from those in high bit. 

You can make a "New document" preset seen below or once you make a document, the dialog should be sticking (next time it will remember all those settings).