For complex notation I had a keyboard distribution with symbols available (e.g., α is alt-a, ∩ is alt + shift + i, ∈ is alt + shift + [) and also made commands to abbreviate, which made it faster than writing (and more consistent). The pace depended on the lecture, but I had no issues keeping up with the teachers speaking/writing pace. If the class was being too complex and I couldn't understand and write in my own words, I just went into "memory dump mode" and wrote whatever and then understood and reformatted it later.
For diagrams I had several options. Simple ones were easy enough to do with Tikz (maybe I didn't get it perfectly on the first try but good enough to fix later), diagrams that had a repeated structure were done with commands, and then for the ones that I couldn't do on the fly I just either wrote the description in text and did them later, or did a drawing in a notebook/phone/took a picture and then replicated it later with Tikz. I could also take diagrams from the web and paste the image.
If you want examples, we actually had all our note PDFs in a shared Dropbox folder [1] (in Spanish, though). Not all of them are mine, but there are a good bunch of them where I'm the main author. I'm specially proud of some notes, like the differential geometry course [2] or topology [3] with a good amount of diagrams (for a math course).
1: https://www.dropbox.com/sh/kbymf37cykz77ha/AADuRd3CoU6UUCZMt...
2: https://www.dropbox.com/sh/kbymf37cykz77ha/AAA1SKV3JLkVPX2nc...
3: https://www.dropbox.com/sh/kbymf37cykz77ha/AABNb9rTsaRzc-3xP...