I'm still quite new to PilotEdge, started by watching a lot of workshops and am now working on the different ratings. Really surprising how much flying online on PilotEdge is different to just flying. There's so much distraction from actually flying the plane

I probably should be able to answer the following question myself after watching Keith's videos, but my brain already removed the information and I can't find it easily in the videos anymore.
My question is related to my approach, which was not really good, I have to admit that. After reaching LAX I got a heading and clearance for the ILS RW8 approach. For some reason, I didn't start descending but remained at 6000ft, my assigned altitude. At one point the controller asked me if I was already descending, vectored me around and told me to descend to 4000ft.
After having thought about that a bit more, I'm still confused. I got vectors and the charts define altitudes at certain points. Can I assume that I'm vectored to the IAF and can descend to the defined altitude on my own discretion? In case of ILS RW8 at KBUR it would be SILEX at 3700ft, but actually 3700ft after "returning" from the procedure turn, which I don't fly when getting vectored.
The question may sound extremely stupid, but this is really the hardest part for me at the moment: what is implicitely included in ATC messages and where do I have to wait (or ask) for a new order. I think in I-1 and -2 I didn't get vectors only but also a new altitude. Which was probably the case for my I-3 as well and I just missed that bit.... I think I was mainly a bit too tired for flying online

What I want to point out is that I'm not looking for "controller did it wrong" or something like that. The controller was really patient, repeated a lot of things because I didn't catch the information the first time and I was actually even surprised that I passed the rating.
Thanks for your help,
Ole