#1 (split infinitives) has absolutely no basis in historical usage. It never has been observed by discerning writers. Ditto for #2 (preposition stranding), #5 (between/among), #7 (possessive with gerund), #8 (starting sentences with a conjunction), and #9 (singular none). I’d hesitate to call these “zombie rules,” because that implies these were once alive. They have never been observed by English as it has actually been spoken and written.
#3 (subjunctive) is a real rule of English grammar, but as the article states, the subjunctive mood is very slowly dying in English (a process that started in Old English), and in its current state is very defective. Good writers will observe the subjunctive, but the article’s advice about not worrying about it is sound for most people. And there is absolutely no need to insist on it in casual communication.
#4 (double negatives) were standard in Old and Middle English, but have long since passed out of standard English. But they survive in dialectal use. So Mick Jagger wasn’t “wrong” for using them. But they should be avoided in formal and semi-formal writing.
#6 (preposition selection) is one I’ve never encountered. I’m assuming its a Briticism. To my American ears either “bored with” or “bored of” is okay, with the latter being somewhat informal. Selection of which preposition to use is highly idiomatic, changing with dialect and over time, sometimes within a generation. One just has to keep a good ear and roll with it.
#10 (try and) has always been standard English, but is avoided in the most formal of writing.
In short, this is pretty good advice. All ten can be safely ignored by the vast majority of writers.
Of the ones the article says one should observe, the article falls down:
The advice for #1’ (who/whom) is good, as is #5’ (lay/lie). Careful writers observe the rules with these ones, although who/whom is often best ignored in informal contexts, where whom can sound stodgy.
#2’ (nonrestrictive that) is not an easy one to explain. The which/that distinction is maintained in edited prose, but ignored by everyone else. There is a historical basis for the rule, but usage patterns changed in the twentieth century, allowing the non-restrictive that. The article is wrong in saying which shouldn’t be used in restrictive contexts. While it’s more often used for non-restrictive contexts, about 25% of its uses are restrictive, even in edited prose. The which/that distinction has never been observed in poetry.
#3’ (compare to/with) is oversimplified. The distinction is maintained in the active voice, but breaks down with the past participle, when either preposition can be used for either situation.
#4’ (collective noun agreement) is advice I’ve never encountered. I’m pretty sure that is not the way it breaks down. Actual usage is highly idiomatic, with Americans tending to use the singular and British the plural, with plenty of exceptions on either side. There’s no simple way to state a rule. You just have to listen and use the one appropriate for the audience.