How good is the Gold game analysis on this site?

Suppose I become a gold member. If I play someone, and then after the game click analyze, how detailed will the analysis be?

Will it anotate move by move what I could have done better, and how my opponent could have got me worse? Will it give any other tips?

And does this site let me set up a position against an expert strength computer and play it?

I have diamond and and when I receive my analysis usually takes a while (it is not instantaneous) I receive a summary report of blunders, inaccuracies, and mistakes.  If you play an inaccuracy, the computer will give you an alternate line and a comment at the end such as "White has a moderate advantage" or something similar but there is no score given.  The analysis is given at ~2500 strenght, or so they claim.

I have not setup a position and try to play it against expert strength so I am not sure if that is possible.

What if I fail to catch my opponent's blunder, but don't lose any material myself? Does that count as a blunder on my part? What is the definition of those three words?

The computer analysis I get as a gold member is stated to be ~2200 strength.  It includes some statements about the change in the evaluation, such as "you went from a winning position to a drawn position."  The analysis will be as detailed as it needs to be, depending on how badly you played.

If you fail to catch your opponent's blunder, that is considered a blunder on your part.  That situation is referred to as a "double blunder."

I also would like to know what chess.com uses as mathematical definitions of blunder, mistake, and inaccuracy.

I am a gold member and I have used it for turn-based games.  I partially agree with ReasonableDoubt.  Most of the time I do not agree with the computer analysis.  But my main gripe is that it only shows ONE alternate move suggestion for your supposed inaccuracy.  

I see you play blitz.  So, analysis may be more helpful to you in that context.  It would basically be a more detailed Blunder-check.  But if you really want reams & reams of analysis, then yeah the best thing is one the engines mentioned before.