Nicole, I cannot answer all of your questions but here are a few things I have used.
NOTE I AM A LOW TECH PERSON and also could no justify big expenditures at my level of Zoom use for now:
1) Just as an aside: Most important to make sure that you are well lit. This is not expensive to do, See youtube for suggestions. Also consider using the "enhance me" feature on Zoom (sorry I have forgotten the name of that option.) It softens the focus by degrees.
2) Yes! Look into your laptop camera lens AMAP. I have taped a hand drawing of two eyes next to my laptop lens to remind me to look into the camera (meaning as if into the eyes of my audience.) It works!
3) For one off, cheap note checking...without buying a Teleprompter... some choices to try:
a) Be honest and tell the audience that you have notes to refer to -- don't try to pretend you are not checking notes because then you just look shifty eyed and guilty and you do not take the proper time needed to read your own prompts confidently.
b) Write out your script or high points on a large white board or flip chart and place it strategically behind your computer/camera where you can take quick glances for reminders of what you want to say without glancing to far off lens. Record samples and find the least distracting placement relative to your eye movements,
c) Print out a sheet and tap it or prop it in a place for easy quick glances. Also no harm in glancing down at a sheet in your hand if you have already told them that you will be checking your notes.
d) Use the split screen feature of Windows 10 (sorry I don't know Apple) to split your view with Zoom session on one side and your scripted document on the other. Use an extra large font on your prompt doc so it is easy to read,
4) Invest in a real teleprompter they are getting cheaper now and some are apps that run on a tablet. See youtube for tons of videos on different things people have set up with their scripts and teleprompters.
Good luck!