When can you start teaching?

To be honest I would say anyone can give advice and teach. But obviously the quality of the advice is likely to be better if the rating is better. So if someone rated about 1000 starts giving me advice I am likely to not take it very seriously. 

Maybe the difference between the teacher and tutee is also important. I would suggest that a rating difference of 300-500 points. So I am currently about 1800 and I would say that anyone rated less than about 1400 would probably benefit from my advice. I might be able to help someone in the 1600s or 1700s but sometimes they may know more than me about a position.

Having said that, rating is probably not the only important factor in a chess teacher. Take golf. Who do you think would be the best person to teach you to play better golf? The best golfer in the world? Or the best golfer's coach. I would go for the latter. Being good at something and being able to teach it don't always go hand in hand. 

I have a passion for teaching. It's my job. Part of it, at least, as a university professor. So I would like to think that I might be quite good at teaching. But nevertheless, I would not feel comfortable teaching anyone within a couple of hundred rating points of me (i.e. 1600+) because my understand of chess is probably not much better than theirs.

You should always stick with personalized advice, based on the games you see.

There's no need to teach chess concepts unless you're trying to explain something established in greater detail, since no matter what you teach at your level, there's going to be some master who's written a book about it. 

Generally speaking, anyone can effectively teach any student who is less knowledgeable than the teacher. One chess tutoring company in my area that teaches elementary school kids requires only a 1200 rating for its teachers, for example. Otherwise, Corum said pretty much the same thing I would have.

After about 1 PM in the afternoon. Before that, I'm not properly awake 

"... I've known many very low-rated chess teachers who are absolutely excellent. ..." - IM Jeremy Silman (2016)
https://www.chess.com/article/view/can-anyone-be-an-im-or-gm

"... Teaching is a skill, and even if you’re rated 1500, you might be just what the doctor ordered for children or beginners of any age. ..." - IM Jeremy Silman (2016)

Teaching is a combination of knowing the material and being able to present it.  In a perfect world, the best teacher would know chess very well (ie, have a high rating) and also be able to elucidate it clearly.  For a variety of reasons, this rarely happens.

One problem, and this goes both ways, is the difference between masters and non-masters.  Masters think about chess in a different way, especially compared to beginners, and they often forget what a beginner thinks and feels about chess.  A master thinks in terms of deep strategy and intricate tactics, whereas the beginner is trying to not hang a piece by move 12.  Does the master really know what to say to such a beginner?  And conversely, does the beginner really know what question to ask the master?  Does he or she know how to then apply that answer?

Personally, despite having a fairly high online rating, I wouldn't feel comfortable teaching someone for the above reasons.  That said, sharing analysis, games, tips, advice and things of that sort?  Those I like to do very much.  It's not teaching, but it may be educational, if you see the distinction.

I was making $400 a week teaching chess back when I was rated (OTB) under 2000.

There are a couple of points to consider:

1. Titled players usually have better things to do with their time than teaching beginners and intermediate players, most of whom will never become super-GMs. A titled player might mentor someone who he believes has the potential to reach the very top, because doing that will become part of the titled player's legacy. Carmine Nigro would be forgotten nowadays if he hadn't been Fischer's first chess teacher. But you need to display Fischer-like talent to capture a titled player's attention.

2. Chess skill is only part of the equation. There are plenty of skilled players who can't break complicated concepts down into simple elements, isolate them, and teach them in a logical sequence. Communications skills and a helpful attitude are also required for a good coach or mentor. In fact, I would say that a mentorship course (or work experience as a professional mentor) is much more useful than a title when you are looking for someone to teach you chess.

I feel that your emphasis on title and rating is misplaced... here is a home-spun homily to illustrate my point:

You and your friend are being chased by an angry bear. You DON'T need to be able to run faster than the bear, in order to get away. You just need to be able to run faster than your friend.

Teaching itself is a skill. You can be a good chess teacher at any chess rating because being a good teacher involves, for example, not talking about things you're not sure of yourself. A good teacher is able to see from the student's point of view, teaching at their level to address their issues, not just giving whatever material they happen to find personally useful or interesting.