1st question: the flight will be somewhat expensive no matter what, but you will fare better traveling if you cut down on the unneccessary expenditures (fly coach, use a hostel). British Airways is an excellent airline that flies out of several large American cities (such as Dallas, Houston or Denver) and takes passengers to their hub at London Gatwick, from there you can fly EasyJet to most of Europe's major cities (Berlin, Rome) or less traveled cities (Minsk, Belgrade, Vilnius), EasyJet is a crowded, cheap and dreadful flying experience but you will save alot of money.
2nd question: In most European countries, the schoolkids are usually learning one or two foreign language (especially English), and anybody working in the tourist industry is going to speak English, so you will generally have most people you meet wanting to speak English to you once they notice that you are an American.
In the countries in central and eastern Europe, I would recommend that you make an attempt to learn the language and learn not only basic phrases, but also how to carry on a conversation. In these countries, people will speak the language to you if you make an effort to speak to them and carry on conversation. Also, in rural areas less people will speak English (if at all) so if you are planning to leave the city it would be wise to learn a bit of the language. In the world today (be it Europe, Asia, or whatever) the young people and the kids do speak English, very few old people will speak English to you (I wonder why).
In cities that have many American and British tourists the odds are that they will converse with you in English no matter what, especially in Paris or Berlin. There is a stereotype in Europe that Americans don't know anything about the rest of the world and don't speak foreign languages, and in Paris and Berlin the odds are that very few people are going to want to converse with you in French or German.