I write and edit on my iPad all the time using the Medium app, so I'm not sure I understand the question. Are you trying to use Medium on a browser?

For Q2: I don't think there is, but the second "quote" option is more centred than any other current formatting tool (but also big and grayer than the regular font, so maybe not good for script-style).

Don't know about Q3. I also started in October (I had a couple stories before that, but barely used the website at all) so maybe there is a better answer to this!