Is it considered plagiarism if I use my OWN answers twice

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.

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.

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.