Well there really is no English equivalent to よろしくお願いします。 I've heard that the closest translation is something like "Please look favorably on me" or "I look forward to a good relationship with you"? The first is kind of weird in English, but the second is totally fine if you want to embellish your meeting. So if you're meeting someone named Jerry for the first time you would probably say something like: "Hello, I'm Tom" Here you would probably shake hands while the other person says "Nice to meet you Tom, I'm Jerry." "Nice to meet you too." This is a formal greeting, such as something that would take place among business associates. One that's more casual, say at a party with friends, would just be "Hey, I'm Tom." "Jerry" "Nice to meet you" though nice to meet you would probably be completely omitted if it was casual enough! Hope this helps, keep learning!

もし単に理由を聞きたい時は"Hoe come?"でいいと思うのですが、私が思うに「なんでやねん！！」の場合はツッコミの意味が強いと思うので、"What the hell"の方が近いと思います。もし"What the hell"が強すぎるのなら、"No way"でもいいと思います。

I think it depends on the situation, but "How come?" Is a good translation.