I thought that was overall a pretty good article. You do start out mentioning avoiding fragments, which is good. That’s more colloquial speech than anything else. It’s perfectly acceptable in the Romance languages except French (it goes right back to Latin where you can leave the subject out of a sentence entirely, but can’t do that in Germanic languages). I’m personally not bothered by run-on sentences. The mind tends to automatically put in the comma or other punctuation where it’s missing. I agree not repeating words like „and“ are fine to start a sentence, but repetition of this should be avoided. But, that’s true about all words in a sentence. You always have to look for synonyms when writing effectively. For example,

„The article you wrote was very good. I wish I had written an article as good as yours.“

That’s fine for beginners. But much better would be

„The article you wrote was very good. I wish I had composed a piece with this quality.“

See how much better this is? I’ve avoided using „article“ twice, avoided using the verb „written“ again and changed „very good“ by using equivalent words. That’s better writing style. I can’t recall everything else you said, but I think you touched on extended modifiers. I think they are very good writing style and can make a sentence beautiful (much more common in German, but pop up occasionally in English.) One that comes to mind is Ann Murray‘s song „Songbird.“ It starts, „Beneath this snowy mantel cold and clean, the unborn grass lies waiting for its coat to turn to green........“ 

The extended modifier building up to the subject leaves the reading or listener wondering for a moment where the subject is and what all the build up has reference to. It’s very effective writing style and carries a beauty to it. 

Thanks Samantha ,it was great article full of the nuts and bolts.I really love these kind of  nuggets which are not just superficial informations but show the ropes in a clear way.

Hi bluebottle, thanks a lot for your kind words! 

If it does, X and Y are two lucky guys :D

Very good tips! Thanks, Samantha. Maybe I will treat myself to a "common denominator"*, too, as I haven't used one in years.

*I hope it has nothing to do with bitcoin?

Great article, With my own students I come at it from a different way. I try to give the empathy for the examiners that will be grading the essays. Imagine you had 50 essays to mark in 3 hours?  I try not to offer actual grammar related corrections.

Thanks for adding the part about commas. To many commas require to much thinking and frustration for the examiner. I ask students to go back to the basics. A sentence should contain one piece of information. Compound and complex sentences just add a better understanding of that information. 

Lets make online teaching the future. Understanding and empathy through language instead of achieving costly pieces of paper that only reinforce hegemonies. Have fun