How will other coins like LiteCoin influence market price of BTC? More generally, in economic aspect, when new currency are issued, and be accepted by groups of people, how will the new currency affect existing currency, ignoring other factors.

Ex. How will BTC affect existing USD?

Ex2. How will LTC affect existing BTC?

Ex3. If a country used to use USD as there currency, but they decide to use a new currency to replace USD, when this currency is becoming more and more important, how will USD be influenced?

It seems that it is more easier to develop new currency for people, not only country, how will BTC find a way out to win the competition with other currency like LTC. What will be the key point in the process?
New currencies that supply similar features to Bitcoins can increase the effective supply to the extent the coins are interchangeable in the market. Even if the other coin is worth, say, one tenth as much as a Bitcoin, ten of that coin can still be used as a market substitute for one Bitcoin.

Depending on the currency's properties, however, it can also increase the demand for Bitcoins, which can drive the price up. If it brings in new users, new merchants, or even new speculative interest, that can be an upward force.

But I think your question about competition, following the question about market price, just assumes that higher prices are good for currencies. I have to disagree with this for several reasons. First, Bitcoin is still in the early stages. It needs to be adopted as a means of exchange to survive long term. Increase in prices can discourage adoption because high prices can increase the fear of a "bubble burst" leading to a sudden drop. Currency risk drives down adoption.

The value of a Bitcoin can be a good measure of adoption because use as a means of exchange drives up demand which drives up price. But the converse doesn't follow. The absolute price of Bitcoin has no effect on its suitability for use as a means of exchange. If it's worth half as much, you just use twice as much.