user13565: What I need
Is there any software/engine/website (preferably free) that can analyze a given game (or PGN) of mine and tell me:

Whether my moves were excellent, good, bad or terrible.
Possible variations at different positions.
Reasons why a bad move was bad, and suggestions for a better move.

What I found
The thing I found closest to that is the computer analysis option on Chess.com , which tells me how many of my (and my opponent's) moves were good, bad and awful, and also suggests better moves in place of my errors. However, despite being rather good, it seems (to me) that it analyzes only the games I play on the site.
Any suggestions?

user13990: I find stockfish pretty good. 
Runs on Windows and Linux.

user4418: The old Fritz 5.32 was (and still is free). You can download it from here http://freechess.50webs.com/fritz.html. You will probably need to have Windows 7 and run in compatibility mode for XP to get this old program to run but it is still quite powerful.
If you want free chess software then http://freechess.50webs.com/index.html is an excellent place to start.

user12449: LiChess.org is free and easy, but you have to register. Almost every interface can give you what the computer thinks is best. 
http://www-lucaschess.rhcloud.com/ is a good program for beginners, but at more advanced levels the computer seems to hang.
Lucas chess has a game analysis.
The output shows current evaluation, best move, your score relative to the best score, and, under indexes, average centipawn loss with other stats.
The program comes with many adjustable parameters.  The main problem, other the the hanging engine, is that it is difficult to find which function you want.  They do have links to many videos showing how to use their program.
If after watching the videos you still have problems, we could start a thread about this problem.

13565: <h2>What I need</h2>

<p>Is there any software/engine/website (preferably free) that can analyze a given game (or PGN) of mine and tell me:</p>

<ul>
<li><p>Whether my moves were excellent, good, bad or terrible.</p></li>
<li><p>Possible variations at different positions.</p></li>
<li><p>Reasons why a <strong>bad move</strong> was bad, and suggestions for a better move.</p></li>
</ul>

<h2>What I found</h2>

<p>The thing I found closest to that is the <strong>computer analysis</strong> option on Chess.com , which tells me how many of my (and my opponent's) moves were good, bad and awful, and also suggests better moves in place of my errors. However, despite being rather good, it seems (to me) that it analyzes only the games I play on the site.</p>

<h3>Any suggestions?</h3>
 13990: <p>I find <a href="https://stockfishchess.org/" rel="nofollow noreferrer">stockfish</a> pretty good. </p>

<p>Runs on Windows and Linux.</p>
 4418: <p>The old Fritz 5.32 was (and still is free). You can download it from here <a href="http://freechess.50webs.com/fritz.html" rel="nofollow noreferrer">http://freechess.50webs.com/fritz.html</a>. You will probably need to have Windows 7 and run in compatibility mode for XP to get this old program to run but it is still quite powerful.</p>

<p>If you want free chess software then <a href="http://freechess.50webs.com/index.html" rel="nofollow noreferrer">http://freechess.50webs.com/index.html</a> is an excellent place to start.</p>
 12449: <p>LiChess.org is free and easy, but you have to register. Almost every interface can give you what the computer thinks is best. </p>

<p><a href="http://www-lucaschess.rhcloud.com/" rel="noreferrer">http://www-lucaschess.rhcloud.com/</a> is a good program for beginners, but at more advanced levels the computer seems to hang.
Lucas chess has a game analysis.<a href="https://i.stack.imgur.com/e52xL.png" rel="noreferrer"><img src="https://i.stack.imgur.com/e52xL.png" alt="enter image description here"></a></p>

<p>The output shows current evaluation, best move, your score relative to the best score, and, under indexes, average centipawn loss with other stats.</p>

<p>The program comes with many adjustable parameters.  The main problem, other the the hanging engine, is that it is difficult to find which function you want.  They do have links to many videos showing how to use their program.</p>

<p>If after watching the videos you still have problems, we could start a thread about this problem.</p>
