Hi Niceweather, sorry to hear your son's diagnosis. I have a ds with allergies to egg and cashew nuts. We were advised to avoid all nuts due to the possibility of cross-contamination - nuts tend to be shelled together in the same place so you really can't be sure that any will be 'safe' for him. We were advised that it would not be necessary to remove all nuts from the house, and dh and dd (no allergies) do still eat nutty cereal and cereal bars etc but they always wash hands and face and brush their teeth when they have done so. I also put any chopping boards, plates, dishes etc that they have used straight into the dishwasher to minimise the chances of nut traces passing onto anything else in the kitchen. Loose nuts would freak me out though - it's the nut dust that worries me, and I don't keep bags of loose nuts in the house.
Ref the skin prick test, I don't think 5mm is all that big ime - ds's raw egg was 13mm! However, all the test tells you is the likelihood of an allergy being present rather than how severe any reaction might be. Ds reacted to raw egg white touching his face with hives where it touched and a red eye where he rubbed it with the back of his hand (he got a tiny bit of egg white on his hand when I was baking) but no reaction at all on his hand 
The severity of an allergic reaction can be influenced by all sorts of factors, for example if your immune system is already fighting an illness, if you have been drinking alcolhol, have recently done exercise, poorly managed asthma, the amount of the allergen ingested and so on and so on...
The Anaphylaxis campaign have a very useful section on their website which explains the law regarding food labelling better than I could, but put simply, a product that contains any of the 14 major allergens as an ingredient must state that on its packaging. There is no law regarding 'may contain traces', but you will find that most companies do give a warning if there is a possibility of cross-contamination during their manufacturing process. However, they don't have to. It is your choice whether or not you heed these warnings, most often it is unlikely that 'may contain' products would cause a reaction, but just because something has been okay the first few times you eat it doesn't mean it always will be.
I've written a bit of an essay here but I just wanted to reassure you that it does get easier. We only found out about ds's nut allergy last October, when he was seven months old, and I can honestly say that I am coping much better now than I did then. I am by no means out of the woods (pnd not helping matters, but CBT is slowly making a difference...) but I am starting to come to terms with the fact that our lives will not be the same as they were before ds and we just have to get on with as normal a life as possible for his sake. The advantage your ds has is that he is able to articulate how a food might make him feel, and he is certainly past the stage of going round shoving everything in sight into his mouth! Again, the Anaphylaxis campaign has a section on its sight for kids as they get older and from what other posters have said, are very good on helping children make the graduation from being protected by their parents to taking on the responsibility for safeguarding themselves.
Good luck, and keep posting for advice - there are some very knowledgable parents on here who have listened to me bang on and on about ds helped me immeasurably since ds got his diagnosis 