Will taking basic courses missed during undergraduate now as a non-degree student help for my PhD applications?
For undergraduate students (or current masters students) applying to graduate school, it's normal that an entire year of their classes are not yet complete at the time grad school applications are submitted (and at a minimum an entire semester). That's usually the time in which students are taking the highest-level classes relevant to their major. Transcripts in my experience always show current enrollment as well as completed courses, even for registered courses that haven't started yet.
If you think you have some weaknesses in coursework areas, then it's definitely better to be able to show you are taking those classes now in some way, even if you don't have grades yet. It's also (and maybe this is a controversial opinion?) sometimes useful to take courses to just, you know, learn something, rather than just increasing admission probability by some unknown percentage point.