أحسن الله إليكم أستاذنا If I decide to wash my hands three times during wudhu, do I have to wash the remaining parts all three times as well, or can I vary them?

You can vary and we will study this in umdat al ahead as there is a hadeeth regarding this in the saheeh that the Prophet did it. So, if u wash your face 3 times and then your arms along with the hands and elbows 2 times this is allowed. But, the best thing to do is to wash all 3 times.