His rooster is pecking at the grain. دِيكُهُ يَلْقُطٌ الْحَبَّ.

It is also said, "Picking at the pebbles." This is said of a gossip.
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The proverb "His rooster pecks at grain" (or, as some say, "picks up pebbles") is used to describe a gossip who gathers news and words from here and there and then spreads them, just as a rooster pecks at grain.
There isn't a direct English equivalent, but some close proverbs and expressions are:
A gossip picks up every little thing.
He has his ear to the ground.
—meaning he gathers news and rumors, even if it doesn't necessarily lead to gossip.
He is always fishing for gossip.
He picks up crumbs of gossip.
The closest English proverb in meaning is:
Little pitchers have big ears.
This is said of someone who gathers conversations and secrets, although it's often used to describe children.
If the intention is gossip and spreading rumors, the closest and most natural expression is:
He is always fishing for gossip.
Or:
He picks up every bit of gossip.
These convey the meaning of the Arabic proverb: He picks up gossip like a rooster picks up grain, then spreads it among people.
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ويروى "يلتقط الحصا". يضرب للنمام.

Let the ugly trait or shameful word pass you by. دَعِ العَوْرَاءَ تَخْطَأْكَ.

(The word "pass you by" is used here with a hamza, as in the expression: "I intended you, but I missed you," meaning I overstepped my bounds.) It is said that this is the wisest proverb the Arabs have coined.
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The Arabic proverb “Let the blind man miss you” is one of the most eloquent proverbs of the Arabs. Its meaning is: Leave aside ugly words, disputes, and shameful behavior, and do not expose yourself to them, for they will pass you by and their harm will not befall you. In other words: Do not stir up trouble, and it will avoid you.
The closest English proverbs to this meaning are:
Let sleeping dogs lie.
— Do not stir up trouble. This is a very common and well-known equivalent.
Ignore it and it will go away.
— A direct expression.
Don't bring trouble upon yourself.
Leave well enough alone.
If you don't stir up trouble, trouble won't find you. (Explanatory formulation)
The best English equivalent of the Arabic proverb "Let the blind man miss you" is:
Let sleeping dogs lie.
Because it perfectly captures the meaning: Leave evil or ugly words alone, without provoking or engaging with them, and they will pass you by unharmed.
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أي الخصلَةَ القبيحة، أو الكلمة الشنعاء وتخطأك - بالهمزة - من قولهم: أرَدْتُكم فخَطِئْتكم، أي تجاوزتكم. قيل: هذا أحْكَمُ مثل ضربته العرب.

.Leave the shortcuts to the cunning thief. دَعِ المَعَاجِيلَ لِطِمْلٍ أَرْجَلَ

"Ma'ajil" is the plural of "ma'jal," which means a shortcut to houses and water sources, as if it were too quick to be fully laid out. "Timl" refers to a cunning thief, and "arjal" means someone with strong, sturdy feet who hardly ever wears out.
This proverb is used to advise staying away from places of suspicion, meaning to leave them to those who are suspected.
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The proverb "Leave the hasty ones to the one with the long legs" means: Stay away from dubious paths and suspicious means, leave them to those who engage in them, and avoid places of accusation and suspicion.
The closest English proverbs to this meaning are:
If you lie down with dogs, you get up with fleas.
— Meaning that associating with bad people or following their ways brings harm and accusations.
Avoid the appearance of evil.
— This is closest in meaning to staying away from places of accusation.
Keep out of harm's way.
Stay away from danger.
Stay away from trouble.
Don't play with fire.
— Meaning, don't expose yourself to what will bring you harm.
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المعاجيل: جمع مَعْجَل، وهو الطريق المختصر إلى المنازل والمياهِ، كأنه أعجل عن أن يكون مبسوطا، والطِّمْل: اللص الخبيث، والأرْجَلُ: الصلب الرِّجْل الذي لا يكاد يَحْفَى.
يضرب في التباعد عن مواضع التُّهَمِ، أي دعها لأصحابها.

The sea is not crossed by rafts. دَأْمَاءُ لاَ يُقْطَعُ بِالأرْمَاثِ.

he sea is called "da'maa," and a raft is made of wood joined together and used for fishing or other purposes.
This proverb is used to describe a great undertaking that can only be accomplished by someone with the necessary helpers and equipment.
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The Arabic proverb "Da'maa' la yuqta'u bil-armaath" means that a momentous matter or a great task cannot be accomplished with weak or insufficient means, but rather requires appropriate resources and support.
The closest English proverbs to this meaning are:
Don't bring a knife to a gunfight.
— That is, don't tackle a great task with unsuitable means.
You can't cross the ocean in a canoe.
— Very close to the image of the Arabic proverb, though not a well-known saying.
Great tasks require great means.
Horses for courses.
— For every situation, there is what suits it.
— That is, every task has its tools and people.
A big job requires big tools.
— A common expression, though not a traditional proverb.
The best and most common English equivalent in meaning is:
Don't bring a knife to a gunfight.
However, if the intention is to maintain the image of the sea and crossing, the closest expression is:
You can't cross the ocean in a canoe.
That is: Don't tackle great tasks with flimsy means or with helpers who are incapable of handling them.
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الدأماء: البحر، والرِّمْث: خَشَبات يُضم بعضُها إلى بعض ثم تركب في البحر للصيد وغيره.
يضرب في الأمر العظيم الذي لا يركبه إلا مَنْ له أعوان وعُدَدٌ تليق به.

He barked wildly, his backside wet. دَهْوَرَ نَبْحاً واسْتُهُ مُبْتَلَّةٌ.

The barking of a dog: A dog that barks, farts, and defecates out of fear of a lion.
This proverb is used to describe someone who threatens someone stronger and more powerful than himself.

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The proverb "He barked loudly, but his backside was wet" is used to describe someone who displays threats, intimidation, and outward bravery, while in reality, he is fearful and trembling before someone stronger.
There is no exact English equivalent, but the closest English proverbs and expressions in meaning are:
His bark is worse than his bite.
— Said of someone who makes many threats but lacks the ability to carry them out.
All bark and no bite.
— This is the closest equivalent to the Arabic proverb.
Empty vessels make the most noise.
— Said of someone who talks a lot and makes threats without any real power.
Bravado is not bravery.
The best and most common English equivalent is:
All bark and no bite.
Because it portrays a person who threatens and makes promises, but in reality is a coward in the face of someone stronger than him, which is exactly what the Arabic proverb “He barks for ages while his backside is wet” means.
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الدهورة: نُبَاح الكلب من فَرَق الأسد ينبح ويَضْرُط ويَسْلَح خوفاً منه.
يضرب لمن يتوعَّدُ من هو أقوى منه وأمنع

Abandon falsehood even when you think it will benefit youدعِ الْكَذِبَ حَيْثُ تَرَى أَنَّهُ يَنْفَعُكَ فإِنَّهُ يَضُرُّكَ،

, for it will ultimately harm you; and adhere to truthfulness even when you think it will harm you, for it will ultimately benefit you.
This proverb encourages making truthfulness a habit.
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This Arabic saying encourages honesty, even if it seems painful or ineffective, and avoidance of lying, even if it seems tempting or beneficial. A similar English proverb or saying is:
"Honesty is the best policy."
This is a well-known English proverb that encourages honesty.
Another saying that conveys a more complete meaning is:
"A lie may take care of the present, but it has no future."
Or:
"Tell the truth, even if it hurts; a lie may help now but harm later."
Similarly, Mark Twain said:
"If you tell the truth, you don't have to remember anything."
However, if you're looking for a common English proverb that corresponds to this Arabic saying, the best equivalent is:
"Honesty is the best policy."
Because it embodies the same idea: honesty is ultimately beneficial, and lying is harmful even if it seems beneficial at first.
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يضرب في الحث على لزوم الصدق حتى يصير عادة.