Re f@g burns etc.
There is good money to be earnt at it. I used to be with SM so was taught the basics and then you trial and learn your self.
I used to know a guy there that would happily repair something like a log burn on an Axminster, repair the backing, sew in the tufts green, red, black etc etc. Take him a week or so but the Insurance co where happy and so was the custy.
As we are all self employed you soon learn where to earn some extra money and when someone says can you fix that its good to know you can.
Carpet fitters arent interested in repairs, they dont get enough for it, they might do border inserts etc where they can seam an edge on etc, but thats about it.
Get some off cuts of carpet and practice by taking the tufts out and then sewing them back in, this way you can see how the carpet is made, you can get curved needles from haberdashers or upholsterers. (Dont practice on Axminsters or Wiltons, thats different work).
Re the corer and a piece of wood, you have to take the carpet up and refit it, with a cig burn just tease the burnt tufts out and re sew in new ones, simplesh, £50 or so if your good enough. I have tried cookie cutters but I found that as its under strain as it comes round it doesnt do a complete circle, it 'comes in' so its not perfect.
I did a course about 15 years ago with a guy called Barry Pierce from Leicester, he had been a CC'er but now only did Rug repairs for the Insurance Co's, he had a shed full of work, re dyed them ,re wove them to the same style and weave, brilliant work. I still have the work pieces we did there and I still show them to clients, hotels etc to show what I can do.
Those of us that have been to the Altec open days have seen there guy do it, dont be scared of it, it really is simple work, the more you practise the better you will be.
Good luck with it.
Murky