I am re-doing a module that I have failed, My first assignment have some questions that are identical to the ones I answered last year, would I be violating any laws or academic practices by copying my own answers from last year and re-use them?
This is a grey area and depends on both the nature of the questions and the specific academic misconduct policy of your university/department/instructor. If you wish to reuse your answers, I would ask the instructor in person if it is okay. If they say yes, I would suggest getting an email confirmation that it is acceptable. That said, while there are many reasons for failing a module, it is probably in your best interest to rework the initial assignments from scratch. If you failed because you were unable to grasp the later material, having a better foundation will help. If you failed because you did not put the effort into the module that it required, this is probably a good test to determine if you are now ready.
In disciplines where answers are discrete and absolute (e.g., most math), if you were right before, your answer SHOULD be the same -- though you should show your work as usual. Where answers are subjective or personal, having the same answer is acceptable, though the result of the work should express any difference in opinion that has taken place over the last term. In cases where there are multiple solutions such as most programming, it may be useful to you (if not necessarily to your instructor) to explore a different method.
Ultimately, there are two routes to go about this:
1) Ask your instructor for their advice (and follow it). Your grade ultimately depends on their opinion, so they are the best source for this.
2) Make your own assumption and stick with it. While it will almost never reflect poorly on you to provide a different answer to the same question (assuming your answer is equally correct), engaging your instructor in a philosophical debate over the objective of education (whether the objective of the course is to learn, or to simply demonstrate knowledge) may require you to appeal your grade if your opinions are not shared by your instructor.
In real life, this question is unfortunately immaterial -- people (especially programmers) borrow work from themselves regularly, and from the standpoint of productivity metrics, generally come out ahead for doing it. Because this relates to the academic environment, this question is best answered by the most direct authority, your instructor.
I once ran into this very situation with a course I was looking to upgrade the mark in, I asked the professor if I could just hand in my assignment from the last time around since it was the same as what he'd assigned. He told me that would be plagiarism, and said I should do the assignment again from scratch as it would be a better learning experience anyways.
Some professors also keep an archive of work from the previous semester or two (at least some of them did at my school) for such occasions. They want to see if something a student has handed in is the same as their work from the previous year or the same assignment as one of their friends. It doesn't happen often but if the prof really wanted to look into it they could.
Just to add another reference, here is an excerpt from the Code of Academic Integrity at Cornell University, saying this is forbidden by default.
Work submitted by a student and used by a faculty member in the determination of a grade in a course may not be submitted by that student in a second course, unless such submission is approved in advance by the faculty member in the second course. If a student is submitting all or part of the same work simultaneously for the determination of a grade in two or more different courses, all faculty members in the courses involved must approve such submissions.
I had to retake a module and its main practical. According to the rules for my university, on no account may you resubmit previously submitted work, as this constitutes self-plagiarism. As I wasn't keen on taking the same bloody practical twice, especially not if I'd have to rewrite, I asked my module organiser: she said carry on, the data will be different, don't worry about the words.
In the end, I used my report from the previous year as a template - the data and some of my conclusions had changed, but I used bits and pieces of my old report (e.g. in the table descriptions). If the answers you would be re-using require very little creativity, then you may not need to edit them very much.
Check the rules and practices for your own university. If you can't find an explicit answer, get in touch with your academic support team or whoever is closest; but unless your work is going to go through plagiarism software (e.g. Turnitin) I shouldn't worry too much about a complete rewrite. You might want to make sure that the person correcting your work is aware that you are retaking the module -- corral them after a lecture if you can, it's usually best.
I sat on a disciplinary board for a student who was in this exact situation a while ago. The student ended up being subject to disciplinary action; the fact that the plagiarized material was their own did not make a difference.
Of course this is also going to be up to the teacher reporting it, and the school's judicial board to decide to uphold or overturn the decision.
Better safe than sorry, ask the professor first, and get an answer IN WRITING.
My university's guidelines actually describe self-plagiarism, here. I think the point would be to go through the whole thinking process of your assignment again and most likely you will come up with a different answer. Sure, it would be fine if it is not completely different but the point would be to not copy it, but rather understand it fully.