Nothing drives me quite as insane as self-proclaimed grammar experts who know nothing about grammar.
#2 is not wrong at all. And even if it were, “towels” is not an object. The verb “be” cannot have an object. It can have a complement, but surely grammar experts like this know all about those, right.
#3 - who says you can’t split an infinitive? That’s a stylistic point, not one about the rights and wrongs of language
#4 - is again fine. The only time a subjunctive would be required here is if the complement were a pronoun (“If I were you”). But if the complement is a noun or noun phrase (“If I were/was ten years younger…”) it’s not required. You might prefer it, but who says it’s necessary?
#5 is fine, if not positively preferable.
#7 - can’t say I’ve ever been bored enough to do a survey, but I would bet my house (were I to have one) on the fact that apostrophes are more commonly used in contractions than to indicate possession.
#10 - no, if you didn’t do nothing, you didn’t do anything. They decidedly do not cancel each other out. Or why would the person say it? One is tempted to think that the speaker knows what they want to express better than Adam Davis.
#12 - ‘they’ is preferable to a singular pronoun here, as it allows for the possibility of a male or female subject. Also “they” is not a “singular object”, as your heading suggests. “What” is the object. “They” is the subject (of the subclause, if you want to get picky). Get it right, man.
Since no-one would ever say #13, it’s a trifle academic, wouldn’t you say?
#15 - yes, the people who make this mistake are the pedants who write buzz feed posts about other people’s grammar when they don’t know much about it themselves.