A seasoned real estate agent can help you with all three of these items. They're experienced negotiators and have written hundreds (thousands) of offers on all types of property. They are also familar with the market and neighborhood so can be of some assistance when it comes to shooting for a low price!
Unless you have a buyer's agent, remember that the agent works for the seller. Make a point of asking him or her to keep your discussions and information confidential. Listen to your real estate agent's advice, but follow your own instincts on deciding a fair price. Calculating your offer should involve several factors: what homes sell for in the area, the home's condition, how long it's been on the market, financing terms, and the seller's situation. By the time you're ready to make an offer, you should have a good idea of what the home is worth and what you can afford. And, be prepared for give-and-take negotiation, which is very common when buying a home. The buyer and seller may often go back and forth until they can agree on a price.