Summary
Danger! Do not mix! 
Chlorinated!
Maybe something to do with not mixing chlorinated water into a drink or something…
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...
Never add it [to anything]! Dangerous! Contains chlorine.
これは泉の水についてかも 
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For the last 3 panels, I haven’t heard English spoken like this before so assuming these are literal translations for learning purposes.
Summary
Don’t mix
Danger
Chlorine
心配するな
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Summary
Do not mix.
Dangerous.
Chlorine.
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Translation
Danger! Don’t Mix! Contains chlorine.
Explanation
This one I’m more confident with my more natural sounding translation. I’m assuming this is talking about bleach products that contain chlorine, and the danger of mixing them with certain acids. This is just a label telling the buyer not to do that.
To make it sound more natural in English, I put the “danger” first.
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translation
Do not mix. Dangerous. Chlorine.
use case
トロールに食べ物を供給するな。
you guys' use case translation
心配するな
Don’t worry.
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Summary
Don’t feed the trolls. 
Not sure every native would know what トロール is in the is context.
Here is a source that has some good info. I’m seeing 荒らし屋 as 荒らす as the main word here with their examples:
- troll：…を荒らす
- trolling：荒らしの行為
- get trolled：荒らされる
Also has your conveyed message as 『荒らし屋は無視しなよ。』
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August 12th Translation
Notes :
塩素系 is a frequently used abbreviation for strongly chlorinated products and bleaches. The full name is 塩素系漂白剤（えんそけいひょうはくざい）
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I think I got the general meaning, not sure about the translation.
Very loose translation
“In order to enjoy food and drinks in the park, please bring your own bento boxes and the like”
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Totally Accurate Translation
You are allowed to bring and eat your bento inside the park. Bon Appétit.
(a bit of interpretation there… ^^’)
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T
As for your bring along lunch (or alike), please eat inside the park.
U
まさかホーマーさんが気づかずに障子を歩き込んでしまった。
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Translation
We kindly ask that you bring something like a bento box if you are to eat in this park.
Explanation
Obviously it is using keigo, and I tried to represent some of that in the language choice. While in Japanese the “if” wasn’t explicitly stated, but it makes it far more natural in English. A more literal translation may be “We ask that you bring something like a bento box in order to eat in the park.”
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I'm unsure about this one
Please bring your bentos and etc. with you and enjoy eating it in the park.
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translation
Please ensure that you eat in the park the bentou and other meal you took with you
use case
@Asherさんと@s1212zさんにもらった面白い説明やリンクを読み込みました。ありがとうございました。
あ!怯える猫は家にちょうど走り込みました。
you guys' use case translation
まさかホーマーさんが気づかずに障子を歩き込んでしまった。
Unexpectedly Homer walked in through the paper sliding window, unnoticed.
4 Likes
Summary
Haha, I don’t think it was ‘unnoticed’ 
The Simpsons - Homer Sliding Doors - YouTube
Tried to convey ‘I can believe Homer went through the sliding door without realizing it’
Now that I see the video, he just didn’t care 
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Summary
Ha ha, yes, funny mistranslation 
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August 13th Translation
Notes :
When sentences have an immense amount of polite language like this, it can actually be easier to work from the end, to the start. よう（に）お願いいたします (to respectfully petition/request), いただきます (the reception of), お召し上がり (humbly eating a meal). Final note 〜ますように usually means that you want something to happen for the person you are speaking to’s sake, not your own.
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translation
In order to prevent the spread of the rocorona please refrain from eating and drinking inside the shop.
use case
船での旅は台風のせいで中止かもしれません。
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