Hello there, @WBaker99 ...
Sorry to see that you are experiencing some issues with the New RCE. We just enabled the New RCE at our Technical College this past Friday, so as a Canvas administrator, I'll be interested in hearing if any of our instructors will have issues with it as they work in their courses. I don't know that I have answers for you on all of your concerns, but I'll try and help out where I can.
1) Unfortunately, I was unable to replicate this in my own sandbox course. Check out this screenshot from my course:

I have circled the button I clicked (Increase indent). For the first paragraph, I was able to click on the button five times to indent the paragraph further to the right. For the second paragraph, I clicked on the same button to indent it three times. None of these required me to go to the HTML side of the page. Might you have had some rogue HTML code already in the content of your page that was, in some way, interfering with your indents?
3) I'm not exactly sure what kind of HTML elements you were wanting to include on your course page, but not all HTML elements are usable in Canvas. This was also true with the old RCE. There is a Canvas HTML Editor Allowlist PDF that details all of the allowed HTML tags in the RCE. If you are using HTML tags that aren't on this list, there's a chance they will be stripped out of your page. Also, this might not be totally related, but have you tried an online HTML editor that cleans up your HTML code? A while back, I wrote a blog about this called HTML Cleanup which may be of help to you.
I hope these resources will be of some help to you. Sing out if you have any other questions about this...thanks! Take care, stay safe, and be well.
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