Wow, where do I begin...? :)
First off, I would recommend anyone to identify in which facets of the game you are lacking (which you have done more or less). I think the biggest factor in improving yourself (no matter if it's football or public speaking or anything else) is to be objectively critical of yourself.
You have pointed out two important aspects of the game, namely technique and mental composure in the game (lets put aside the physical composure for a second). These are two very different aspects, which require different approaches to improve. What's common between them is practice. The more you play the more accustomed to playing you will get. This doesn't mean that you will automatically get better at playing, but you will undoubtedly feel more comfortable on the pitch. That aside, let's take a look at it one thing at a time:
The technique: this is obviously the hard bit. Shooting, dribbling, heading, accurate passing/crossing are all very dependent on good technique. Technique on the other hand is built on being proficient in the fundamentals, like which side of the foot you should use in order to send the ball to different directions.
Another good example is how you control the ball when it comes at you rolling or flying. You might have seen some players get really high/fast balls without a bounce, that for instance requires good skill and control, typically sign of a player who's got the fundamentals down. As @gbianchi has pointed out, this type of fundamental skills are much easier to learn at younger age, then it'll just sit in the backbone.
That said, how can you improve? I cannot give you an exhaustive list but here are a couple tips:
A good shot always starts with a good composure, if you are off-balance or haven't placed your support leg at the right position, your shot will ultimately be a wasted effort.
practice with using different parts of your shooting foot (inside, tip, outside, heel...) in front of a wall. Just to see how the ball reacts to your shot/pass. Likewise the point of contact with the ball is also very important. You need to get a feel for how the ball will react to different kinds of contact with your foot.
to increase your composure on the ball, ask a friend to help you out with the following drill: put one foot on the ball (the one you feel most comfortable with). Then ask your friend to try to get to the ball, while you just move the ball away from him, using your own body between the ball and your "opponent" (check this video out)
The mental composure: This bit could be easier than improving your technique, since it's entirely in your head and have almost nothing to do with your body.
First off, as I said the more you play the more comfortable you will be with the ball. Most important thing you need to learn/figure out is to not be afraid of the ball. I cannot stress this enough. Even professionals end up being afraid of the ball at times, avoiding the ball and responsibility that comes with it.
Avoiding the ball is a terrible thing in two ways; 1) it will seriously hinder your improvement 2) it will leave your teammates in tough spots at times. There is no such thing as keeping a low profile in this type of team sports (especially in 5-a-side), you should always be available to take a pass from a teammate.
Once you have established that getting the ball is not a thing to be scared off, you should concentrate on reminding yourself that making a mistake is not the end of the world. This is very crucial to understand that mistakes are part of the game, and as it happens there is only one thing you should focus on, making amends. You lost the ball by a bad pass/unnecessary dribble? Win it back! Cleared the ball towards an attacker? Cover the shot! Team sports are all about taking responsibility, once you take responsibility for your mistakes your self-confidence will improve as well as your teammates opinion of you.
All that said, here are a couple of tips to reduce your stress while playing defense:
Last man in defense? Don't go dribbling; last man plays safe: ALWAYS!
Unless you are extremely fast in your reaction times, don't rush the incoming attacker. Back up slowly covering the zone and the shot. Attackers (especially those who are skilled in dribbling) will almost always try and trick you into committing to a false move, and go the other way.
When outnumbered your action kinda depends on how good your goalie is. If the goalie is confident against long shots (i.e. has good reflexes), cover the run and the pass. Otherwise cover the shot.
Game intelligence: probably the hardest thing to improve. It's easy to "read" the game, sitting in a sofa at home, seeing the tele-cam cover half of the field from above. It takes much practice and honestly a bit of talent to be able to read the game properly while playing (please note that I do not claim to have the talent myself :))
I almost exclusively play defense in futsal (indoor 5-aside) and I think it definitely helps with game intelligence. You learn to observe how others play. Paying attention to tendencies in different players' game is a great asset for a defender/midfielder. Oh, and don't just watch the ball, as a defender you should always know where your opponent is. "Is he still where he was last I checked, or is he taking a diagonal run?"
When playing as a more attacking role; keep in mind that you don't need to do something elaborate to be effective. I personally never felt particularly comfortable with dribbling, instead I prefer short quick passes, 1-2 plays as well as through passes to a teammate, or taking a deep run to outflank the defense.
Practice is king! Play more: practice what you are bad at before/after a game, stick to what you are good at during the game. Take initiative, talk to your teammates/friends on your progress. Most of all, make sure you have fun when you play. If you treat it very seriously you'll probably get too nervous. It's supposed to be fun, right? ;)