You're not being unreasonable to be worried - of course not. Every mother is worried when her child has an anaesthetic, you are handing your precious children to the care of someone else and your fear is understandable.
It is not helped with irresponsible friends (GP or not) saying they wouldn't let their children have an op (maybe her kids don't need it - I wouldn't let mine have their tonsils out at the moment, but that's because they've never had a day's sore throat in their lives and there's no indication to do it) or saying that 7 is the worst age (which is complete rubbish).
Tonsillectomy is definitely worse in adults - they are in more pain afterwards and the post operative recovery period is of the order of 1-2 weeks as opposed to 1-2 days in children.
I have not met a single anaesthetist who would ever say to a patient "Things go wrong more often than you'd think" - mostly because it's not true but also because it's completely bloody irresponsible.
Unfortunately everything in life has a risk associated with it (there are several injuries a year related to putting on socks) and part of the surgeon's job is to inform you of those risks so you as the responsible adult can decide if the risk of surgery outweighs the risk of leaving things as they are. From my perspective the fact that it's impinging on his ability to cycle, do sport etc with family and friends would be a pretty big incentive to getting it done but I know everyone's attitude to risk is different.
MilaMae - what will happen. You will chat to the anaesthetist on the ward beforehand. They may listen to your son's heart and lungs - a benign murmur is nothing to worry about but they may want to give antibiotics during the procedure (some surgeons I have worked with do, some don't). Your son may be given a premed (painkiller mixed with sedative) if they feel he would benefit from it (again, I tend to use it a lot but I know some of my colleagues don't).
When he comes to theatre he will sit either on your lap or on the table depending on how he's acting. They will put a small peg like monitor on a finger or toe to measure his pulse rate and oxygen levels. They then either put a small drip (via a needle) into the back of his hand and give him the anaesthetic through it, or they hold a facemask with oxygen and anaesthetic gas mixture gently over his face for him to breathe. Either way, you'll be with him as he falls asleep. Once asleep, you'll be asked to leave (and you will probably cry in the corridor) - if a drip wasn't put in to get him off to sleep, they'll put one in then. He'll have a breathing tube put in to get oxygen and anaesthetic into his lungs and the rest of the monitoring put on (ECG dots for heart rhythm, blood pressure cuff which cycles every few minutes).
The surgeon will take out the tonsil in question, during this time the anaesthetist gives medicine for pain, sickness, to reduce swelling etc through the drip. At the end, the anaesthetic is turned off and as your son breathes it out and breathes in oxygen, he'll wake up and spit out the breathing tube.
Risks I quote to parents before the anaesthetic are: waking up with a sore throad, some post operative sickness or vomiting and very rarely, damage to teeth (caused when we open the mouth to put in the breathing tube - occasionally wobbly teeth come adrift. Very rare though!) There is also a very rare chance of being allergic to one of the anaesthetic components - estimated as occurring every 1:1000 to 1:20000 anaesthetics (yes it's a wide range) - the reactions vary from an itchy rash to anaphylaxis which can be serious. However you have to remember that these are extremely rare and that anaesthetists are trained to recognise the signs of any adverse reaction and treat them immediately.
Your son will wake up in recovery with the peg monitor on measuring his heart rate and oxygen levels and a clear plastic oxygen mask on his face. He is likely to be extremely grumpy, thirsty and disoriented - all of these improve when you come up to recovery to cuddle him and he is given a drink.
Nothing anyone says will allay your fears entirely and ultimately it is your choice - nobody will force you into signing a consent form and nobody will mind if you change your mind. You don't need a virtual slap and you shouldn't cancel or not based on the responses you get here.
Have a virtual instead!