So it seems like I can pretty much choose any time I want to PSYCH 1X03 and 1XX3 with all the options I'm given (once they don't conflict with my other courses). So is there an ideal time for these courses? From what I understand, everything is online for the first term, so does the timing of my PSYCH 1X03 core matter (there's a location that shows up on my mock timetable, so I'm probably completely off)? And is better have have my PSYCH 1XX3 tutorial later in the week (I heard it's better that way so you're not rushing to know the information)?

Sorry, for all the questions but it'd be greatly appreciated if someone could offer some insight.

Also, does it matter for any course if the tutorial comes before the core in the week (e.g. Tutorial at 1:30 pm on Tuesday and then core at 3:00 pm on that same Tuesday)? Or is it just better to have one come before the other?

There is no core for Psych 1X03 - just tutorial.
There is a core for Psych 1XX3 though.

From personal experience, I tried having a tutorial a day before the weekly quizzes and also a couple of days before.
I found it more useful to have the tutorial couple of days before the quiz (which is on Friday), because you need to know the content/online lecture content in order to fully understand and participate in class (which counts for grades btw). If you have it later on in the week, more closer to the quiz date you will find that you are rushing to finish it. Either way, depends on your schedule and personal preference too.

Also I usually kept my tutorials either mid-day or afternoon because I would listen to the online lecture in the morning before my tutorals.

And no it doesn't really matter if you have the tutorial before the week. But some of the questions prompted in the tutorial come from the live lecture for Psych 1XX3. So its better if you attend live lecture, listened to the online lecture THEN go to tutorial. Optimum way to make use of your time.