A: No, you're not right in thinking that. An employer can hire someone else right after you leave, but it will cast doubt on the real reason for firing you. If this happens, you can bring a claim for unfair dismissal and if the employer cannot prove that the redundancy was genuine, but the circumstances have now changed, you will definitely be successful with your claim.
What you described is one of the sly ways in which employers avoid getting caught when using redundancy to unfairly dismiss someone. They either wait a while before hiring someone new or they re-name the position.