The criteria of how many points won/lost after games?

They use the Glicko system.  I'll go get you the article, but basically when you first start out your rating bounces up and down like a gymnast on a trampoline.  Later on, not so much, more like the rise and fall of a fat man's belly taking a snooze.

https://support.chess.com/article/210-how-do-ratings-work-on-chess-com

lol

There are many factors that go into how your rating changes after a game:

1. Your rating at the time the game ends

2. Your opponent's rating at the time the game ends

3. Your RD at the time the game ends

4. Your opponent's RD at the time the game ends

What's RD?  It stands for Rating Deviation, and is basically a measure of how accurate chess.com thinks your rating is.  The larger your RD is, the less sure chess.com is about your rating.  You can think of it as your true rating is probably within your rating plus or minus your RD (e.g., if your rating is 1200 and your RD is 100, your true rating is likely between 1100 and 1300).

Having a large RD means that your rating is going to change by more.  Having a small RD means that your rating is not likely to change by much.

If your opponent has a large RD, your rating will change by less, so as to not punish you for the inaccuracy in your opponent's rating.

If your opponent has a small RD, your rating will change by more because chess.com is more certain that your opponent's rating is correct.

Your RD will decrease if you perform "as expected" - if you win games you should win and lose games you should lose.

Similarly, your RD will increase if you perform opposite to expectations.

Your RD will also slowly increase over time, as the algorithm doesn't know if you've been improving or slacking in your chess studies.

In general, when you win or lose, you will gain or lose points in proportion to the strength of your opponent.  

I've played lots of blitz and rapid so my glicko is low, meaning there is more certainty in the accuracy of my rating.  For me, I observe if I beat someone around my own rating (plus or minus 25? 50? not sure), I will gain 8 rating points.  If I win but my opponent was rated 100 points lower, I might only gain 5 rating points.  With much higher rated opponents I might gain 10 or 11 points.  

 I think that your own Glicko score affects this generalization, but not your opponents.  

For example, if you are new and have an estimated rating of 1200, but not much real games to verify your strength, then you might play another 1200 player and if you lose, you will drop 50 or 75 points.  As you play more, the data becomes more certain and the score will fluctuate less.

But for me, if I beat someone my own strength, I will gain 8 regardless of my opponents Glicko.  His might go down 8 or go down 50, but his Glicko doesn't effect my gain or loss. 

If the opponent has a high Glicko (indicating great uncertainty in their actual playing strength) then you will gain or lose fewer points... since the opponent might really be either stronger or weaker than you are.

It makes sense that it would work that way, but based on my observations, I am not sure that it does.

For example, If I play someone 150 points above me and win, I would normally gain say 11 points.  But if he has a high glicko, he might drop 100 points and only be rated 50 above me after the game.  So would I gain based on his pre-game rating, (+11) or post game rating (+9)?  

It is not fair in certain extend because the lower level won, you lose more points than the higher level, that is why people don't want to play with the lower level, and the end result is you was labelled - not a good sportmanship, and punished.

why is it when i play rapid games that the points on offer are plus 27 for a win and minus 25 for a loss, where as my opponent has plus +8 and -10? 

is it because i havent played enough games and so my points plus or minus on offer are much larger 

Yes, the larger change in your rapid rating was mostly because you have only played 7 rapid games since last April.   The statistical measures that look at your rating accuracy mostly look at how how often and how recently you have played.  Since you haven't played much, they say that your rating is very likely to be relatively inaccurate.   As a result, the ratings changes you see will be large until the measures say that your rating is deemed pretty accurate.  The main factor driving it is how much and how often you have played.  

Read post #7.  It was explained well.

"What's RD? It stands for Rating Deviation, and is basically a measure of how accurate chess.com thinks your rating is."

AND here is the problem. All this work to get a "rating" but once again a game comes with a secret rating that affects you even more. Always has been and always will be a crappy system

my brother just lost 42 ratings in one game. Is that normal?

Depends what the Oppenents Rating is.

Opponents*

Yes. It is normal when someone is new or hasn't played in a long time.

This was all explained earlier in the thread.