trading pawns and minor pieces

It's a good question.

Unfortunately the question is nearly as complicated as "how do I play chess well?"

To get a good answer you'd need to post a game you played, and ask about a position where you were unsure what to do.

The general concept, for beginners, is that you trade pawns when you're lagging behind in development, and you trade pieces when you're ahead of your opponent in development. The concept behind trading pawns is that you allow your pieces more freedom to develop to their best squares (mobility), and that trading pieces, both major and minor, hinders your opponent's piece synergy/dynamics and possibly ruins their pawn structure. That is why, often times, Grandmasters choose not to accept minor piece trades (as in, they don't recapture and treat the intended exchange as a sacrifice). I saw a King's Indian game with Carlsen vs. Polgar, and Carlsen purposely declined a piece exchange.

PS: I don't recommend that you use the "Analysis" feature if you're a beginner. Just play without it and get a "feel in the blind," so to speak, about your playing style. Remember, the "Analysis" is meant to give you a computerised version of what you should have done, so don't take it too seriously.

Mind explaining, with a tad more courtesy this time? I'd love your correction if I am indeed wrong. You can help mistaken people instead of shooting them down, mind you. 

Study chess strategy. Trading pieces when no tactic exists is something that effects probably every chess game ever played, excluding opening blunders and traps.

Mariners234 has a point. But even if you don't have a specific game in mind, learning some basic strategy beyond "rules-of-thumb" would be helpful.

Strategy isn't rules-of-thumb, but rather learning how to apply long range plans in your game. Doing that will give insight to how and why you might chose when or which piece to trade.

A beginners book on strategy might do wonders for your game.

The rule of thumb is to trade pawns when you're behind in material. This is because the drawing margin of pawnless endgames is much higher. For example pawnless rook + bishop vs rook is a draw. There are even fortresses in pawnless queen vs knight + bishop.

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But also, trading pawns when behind in development is bad, because this open lines, and open lines favor the side with more active pieces.

The rule of thumb is to trade pieces when you're ahead in material. This is because there are less drawing chances in K vs K and in pawn up minor piece endgames... and in general the less dynamics there are in the position, the more static features (like material) will be decisive.

The rule of thumb for having less space, is you trade pieces (not pawns). With fewer pieces, you're less cramped.

A rule of thumb for someone defending against an attack is to trade pieces for pretty much the reasons you listed.

That's completely ridiculous.

You are still a big beginner with approx 600 rating.

A beginner schooling another beginner is funny.

I hope you improve with your own logics.

I think learning some very basic strategy will help a beginner visualise what rules-of-thumb can apply in a position. That would make rules-of-thump more clear in application.