For #1, try to explain it to a friend, preferably in person, possibly via a chat app, but definitely not via email. Then base your writing on the way you explained that. (But like, with complete sentences.) This is the best method I know for shaking off the instinct to sound like other people's writing (i.e: like technical papers) instead of just explaining things.

Here's three examples of excellent explanations via very different techniques:

[1] https://pomax.github.io/bezierinfo/ - Bezier curves, exhaustively technical but well-indexed and just really well explained

[2] https://directtovideo.wordpress.com/2011/02/25/ceasefire-all... - Advanced and unorthodox rendering techniques, narrative format, basically the opposite priorities of a paper (assumes you can fill in the gaps on how, details more what worked and why it's being used)

[3] http://archive.is/XjbUy (supposed to be at qntm.org/gay, but apparently being rewritten) Database normalization principles via the lens of making a database handle gay marriage, humorous

Also, if you're explaining sequential bayesian filtering by any chance (my specialty), I'd really like it if someone actually wrote down the awful formal version with the point-wise Bayes Theorem and the giant integral convolving over your state transition function, then explained how particle filters / kalman filters / hidden markov models get around how awful that is. It's how I introduce the topic at work but I don't have my slides handy out here in the real world.