>can hear it's barking clearly and loudly
This technically isn't incorrect, but people would MUCH more likely say "it barking" than "it's barking"
>"enough!" I said with an annoyance
This one doesn't make much sense, but it does remain clear that you're annoyed. To say something "with an annoyance" means that you're saying it as something annoying is with you, which is weird. An "annoyance" is something that is actively being annoying, and is not a feeling. Say "I said, annoyed" instead.
>plan about sniping it with a 50.cal airsoft
"Plan about" doesn't really mean anything. Say "plan to" instead.
>inspect them for 8 days
Inspecting a person pretty much means you're inspecting their body, which implies they're dead or you're a doctor. I guess you're trying to say that you watched them and observed what they were doing, but you should also say that you inspected what they were doing, rather than inspecting them (again, that implies you are doing stuff with their bodies).
>(((they))) sleep at 12am and keep the doggo at garden
"At the garden side" could be used in some rare circumstances, but not in this once. Anyway, 99% of English speakers are going to say "in the garden" here. "At garden" would always be wrong.
>get stolen immediately
*gets
>never heard of him since a month
Saying "never heard of him" in any context means that you do not know of the existence of the dog, and never have. "Since a month" is also wrong, it should be replaced with "for a month" or "in a month" depending on the context.
The sentence should read "Haven't heard anything from/about him in a month" or "haven't heard him in a month", depending on what you're trying to say.
I hope this helped. I was quite harsh (I always want people to be harsh with my German, so this is the attitude I take) but hopefully you learned something.
Also, your English is more than understandable. I'm sure you'd have no trouble in English speaking countries. ;)
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