"This tastes bad."
I'm not 100% sure, but I think if you use これ you have to use は, because you're establishing that これ is the topic, you are going to talk about "this". If you don't use これ (because it may be obvious that you're talking about "this") you don't need the topic particle (は). Please feel free to correct my english or my japanese because I'm just learning :)
The は is not necessary or even correct (formally, in the duolingo fashion) without the これ before it. Otherwise the particle (は) would have no subject to refer to (here it's これ). Omitting both the subject and its particle is fine as we see, but including the particle without its subject is like saying "Is bad" instead of "This is bad" (not the literal translation but it illustrates the point)
Not sure if it's intentional. The kanji for "mazui" is not generally used, but I think it should be accepted anyway. As examples, I could find two media occurence of the word. Episode 66 of the anime Digimon Fusion is "おいしい？まずい？デジモン・ラーメン勝負！"¹ and the first episode of the Japanese drama Bartender is "嵐を呼ぶ男VS伝説ホテル王…永久にまずい酒"².
kono, sono, and ano must be followed by a noun immediately after. they need a noun to specify. for example: " あの人は誰ですか？" the あの is followed immediately by 人, which is the noun. you're specifying that you want to know who THAT person is. - kore, sore, and are are followed by " は " normally. it's a broad way to describe objects. for example, " このももはいくらですか。" is asking how much specifically that peach is, and if you used " これはいくらですか。" you're just asking about a non-specified object. i don't think you would use something like ” これはももがいくらですか。” i hope this makes sense! i'm also only a student myself so anyone feel free to correct me.
I believe if you use これ ("kore"/this) you have to use は for the full sentence これはまずいです ("kore wa mazui desu"/this tastes bad).
But if it's implied from context so the other person knows what you're talking about you can drop the これ and associated は altogether and just say まずいです ("mazui desu"/tastes bad).
I don't think これまずいです (the full sentence without the は) is technically correct, but I'm learning too so correct me if I'm wrong.
You either omit the entire thematic topic (これは) or none of it. Its improper to write これ alone, although in casual speaking it may be ok to omit the は particle, (you'd be understood and some native speakers will do this from time to time) it's not correct in writing.
Duo accepted まずいです for me. I would expect it not to accept これまずいです because its missing a necessary topic particle.