To be honest, I've never used this phrase, but I believe it means: "Be completely honest with me" You use it when you want to change the tone of the conversation suddenly, and become very candid or open with the person. If you are talking with your friend about something lighthearted, and you really want to tell them something that's been on your mind, you might say "Alright, level with me for a second" My explanation might be hard to understand. I'm sorry I can't speak Ukrainian or Russian at all. Hopefully, someone who speaks Ukrainian or Russian can explain it to you.

I just realized that your question asked for examples... Example 1: You're working in a company and you know that there is a spot open for a promotion. You are one of the candidates but you're not sure if you have a real chance at the spot. You could say to your boss "Look... level with me... do I have a real chance of getting this promotion?" Example 2: Your friend offers to sell you his car for 20% less than its market value. You don't think he's serious or maybe there's something wrong with the car. You could say "Look... level with me... are you really going to sell it to me for that price? Is there something wrong with the car?" Example 3: You think your girlfriend is interested in another boy. You ask her friends "Level with me... is she interested in him?"

When constructing buildings, it is important that things be "level". If they are not level, then there will be problems with the building. Being level is also important in playing pool or billiards. In general, being "on the level" is considered being honest and straightforward. So, asking someone to "level with you" is asking them to be honest and straightforward. The Free Dictionary notes that this phrase is often used when the information being solicited may be unpleasant to the hearer... http://idioms.thefreedictionary.com/level+with