1 - Is it an expectation that anyone within the organisation can complete a corrective action form? Or should it be directed through a central location e.g. the service desk for them to complete?
Answer: the standard only requires that corrective actions are performed when needed after a nonconformity is encountered. How to handle a corrective action is an organization decision, and both approaches you mentioned are valid ones. You only have to ensure that people who handle a corrective action are properly trained in doing so and that results of any corrective action are retained as documented information .
2 - Would it be appropriate to post the form on our intranet and direct all our people to it for them to complete and then submit the form?
Answer: In terms of the standard this point is indifferent (this is another "how" situation, and the standard only defined "what" must be done), but for an organization's operational purposes this is a good idea, because it makes easier to find the form.
3 - Presumably this is to evidence continual improvement?
Answer: Yes. Together with evidences of implemented opportunities for improvement, documented information about corrective actions are evidences that the management system is being improved over the time.