Niin metsä vastaa kuin sinne huudetaan. / The forest answers in the same way one shouts at it.
This proverb means that your deeds have their consequences and the English equivalent would be “What goes around comes around”.
“Sitä niittää, mitä kylvää” comes from Bible: “You reap what you sow.” Other proverbs with the same meaning are
“siten makaa miten petaa” / As you make your bed, so you must lie on it and
“sitä saa, mitä tilaa”/ “you get what you order”.
Nälkä kasvaa syödessä / The hunger grows by eating
The more you eat, the more you crave, the English equivalent would probably be “I am a bottomless pit”. This applies also to other good things in life besides food.
Apparently the same idea exists in French “L’appétit vient en mangeant.”
On the other hand “ei makeaa mahan täydeltä” / “don’t fill your stomack with sweets” means that you shouldn’t have too much good things.
Hänellä on ketunhäntä kainalossa. / He has a fox tail under his arm.
The cunning fox is a metaphor for dishonesty, so hiding a fox tail refers to some kind of dodginess. A similar idiom exists in English: “a wolf in sheep’s clothing”, and it’s also a common saying in Finnish: “Hän on susi lammasten vaatteissa.”
Another idiom related to suspicious things is “Juttuun oli koira haudattuna.” / “There’s a dog buried in it.” In English, you’d probably say something like “there’s something fishy about it” or “I smell a rat.”