"I will play with her today."
To be fair, I think he's directing his advice to those learning English, not English native speakers. I don't think he's complaining about the translation. It's a weird feature of English (I haven't come across this 'play' problem in any other language) that is worth pointing out in the context of adults "playing" with adults.
"Playing (with someone)" is not the same as "playing something (with someone)". You wouldn't even use あそぶ to translate the latter into Japanese, normally, it'd just be する "do". So those examples aren't really relevant.
Still, while I do think translating あそびます as "play" is a bit awkward in English when talking about adults (who might be e.g. singing karaoke or drinking at a bar), I tend to agree with Frrost that for the purposes of Duolingo it's easier to just accept it... That is, it's up to the maintainers of the Japanese course whether they want to accept things like "hang out" or "enjoy oneself", but I'm fine with them keeping "play" as the preferred translation even if it's kind of translationese. This isn't an English course, after all.
a) That's not what "subject" means in grammar. The subject of this sentence is (the unstated) "I". (This may seem pedantic, but to understand explanations of Japanese grammar it's important to avoid confusion between "subject" and "topic".)
b) As for marking a time or location phrase as a topic with は, that may or may not be appropriate depending on the context. Saying it "should be there" as a general rule is incorrect (though it's true it'll generally work for these contextless examples).
I'm very confused as for the difference between the "と" and "も" particles. I gather both can construct sets or enumerations, except that "も" can imply the existence of more elements than stated by the speaker. Is that right? Is that the only difference? Why is "も" wrong in this context?
Yes but in English that's generally redundant, whereas from what I've seen it's common to use 一緒に to make it explicit that all parties are taking part in the same activity. Even in English "I will play with her" could technically mean the other party is not actively involved, though that would be...creepy...
To anyone who believes 'playing' to be awkward. Go give your inner child a hug and open your mind/heart... next time you 'hit up' your friends, I dare you to ask them if they wanna come over and play or go out and play- WITHOUT any dirty thoughts as thoughts DIRECTLY affect the way our words come out. Try it innocently and I bet they'll laugh and say 'Sure'. Congrats- you'll be bonding even more in no time. Your welcome. ^_^
Is 彼女と遊びます、今日は wrong? I forgot to add the today at the beginning where it usually is, and I thought maybe this would be alright, but it was marked wrong. Like maybe it's a version of this sentence where the speaker is talking about playing with her and only remembers to point out that it's today afterwards? Or does no one talk like that in Japanese hmmm. I don't know
Something I have been wondering: if I wanted to make 彼女 the topic in this sentence, while also indicating that it is her I will play with, what would happen with the particles? Would you use two? As in, 今日彼女はと遊びます。? Something tells me this is completely wrong as the 今日 feels like it should have a particle...
今日 can just be an adverb describing when you did something, so no, doesn't need particle. I'm not sure there's a natural way you could make "彼女" the topic, but it would seem you could make 彼女と the topic, and 彼女とは今日遊びます might be feasible, but you'd really need a native speaker to confirm, and I doubt Duo would accept it.