Possible duplicate of How do I use the comment notification system?

Unless recently something has changed, images are not uploaded to MO, but only linked to. -- To which site did you try to upload the image?

I'd say if you think that the question would be on-topic and likely well-received on MathStackExchange, then rather don't downvote, but vote to migrate -- commenting is optional, but usually good if nobody else has commented yet. Downvotes are rather for questions which you think are bad, unclear, not useful, written down in a sloppy way or lack necessary background information.

I think a main point here is that a signature below a post discourages any editing of that post, as an edit would change what the signing person literally has said.

Feature request or discussion?

Isn't peer-review quite orthogonal to the purpose of MathOverflow? -- I'd rather think such feature may be a worthwhile addition to the arXiv, but I can't really imagine how to sensibly integrate this into MathOverflow.

In the latter way, you can also enter e.g. chinese text: 曼弗雷德·魏斯

Just type it in like any other text, without using MathJax or any other fancy things: Gâteaux. Or paste it from somewhere else if your keyboard doesn't easily permit entering an â.

If the user name sounds like a real name, then I think it should be the real name of the owner of the user account; similarly, if the picture shows a human, it should show the owner of the user account -- everything else is at least bad style. Also, I think one should not choose user names or -pictures which are designed to be controversial or offensive.

Terminology is either standard or it is defined before it is used. -- In the former case you can just google for the definition, and in the latter case you need to look up the definition in the book or paper where it is used. I think in none of these cases asking for a definition is on-topic on MO.

You can always ask an author directly, provided that the author is a living person and you have the contact data, and you are always welcome to ask on-topic questions on MO. Questions of the type you suggest could sometimes be taken as "too localized" for MO -- but apart from this, what kind of advice are you hoping for?

In a case like this you can always flag for moderator attention. -- Moderators can migrate questions to any SE site.