In English, your first proverb would be translated as "There is no smoke without fire".

There are a lot of proverbs in Russia.

Here some of them:

Economy is a good servant but a bad master.

Your elbow is close, yet you can't bite it.

God gave, God took back.

Third time is a charm.; Third time is a lucky.

Hey I'm from Indonesia too. Don't forget this proverb

"Kuman di seberang lautan tampak, gajah di pelupuk mata tak tampak" in English => "The bacterium across the sea is seen, but the elephant on the eyelid is not seen."

It means = The faults of others are easier to see than our own faults.

An English version of your third proverb would be, "When in Rome, do as the Romans do" (or, more often shortened to simply "when in Rome..."). It also means to adapt to the customs of the place where you are.

"Out of the frying pan, into the fire" - something was bad and instead of it getting better, it just got even worse.

"Better the devil you know than the one you don't" - sort of the opposite of the one above. Maybe something isn't that great, but maybe an alternative would be worse.

"The early bird gets the worm" - it pays to be the first, the earliest, etc. because you'll reap the rewards while others are still sleeping, etc.