1. The jump leads catching fire is normal I’m afraid – most of the cheap leads they sell in petrol stations are far too thin for the job and overheat due to their high resistance. What’s the point in having a jump lead then you ask? Well Car Machanics Magazine raised the same question, and the manufacturers said that the leads are not intended for jump-starting the car, instead they should be used to top-up the battery overnight… which is rubbish.
I have always made a point of buying heavy duty thick copper jump leads, which you need to shop around for, and they do the job perfectly and without overheating.
2. As for your second problem, i.e. the positive terminal getting hot, it could be that the started motor is drawing too much juice from the battery, which would indicate an electrical fault with either the motor itself or the solenoid, or there may be a short circuit, and in this case it could be the starter motor but it does not have to be that – anything that causes a short circuit further before the fusebale link box will have similar a effect. The reason the starter motor is the main suspect for a short circuit is that it is one of the very few electrical components in a car that are NOT protected by a fuse - any other component failing would blow the fuse before the battery terminals overheat.
However I think that the symptoms you describe are compatible with a bad battery connection – a loose or corroded terminal connection would (a) overheat due to high resistance and (b) not supply enough current to rev the starter motor properly again due to the losses over the resistance of the dodgy battery terminal.
I suggest that you try first cleaning the battery terminals, make sure that the wires and connectors are clean and sound, and if the problem persists try another battery.