How much money can a new Country print for their local circulation?

Question

How is their dollar peg to the USD and why to USD?

Answer 1

As much as they want.
The problem with printing too much currency, though, is that you end up with an ever-increasing money supply chasing the same amount of goods and services, which results in price inflation. That, in turn, reduces the value of your money.
A few historical examples would be Germany in the early 1920s (You have probably seen the photos of workers with wheelbarrows full of nearly worthless banknotes), Yugoslavia in the early 1990s (perhaps you have seen the 1993 Yugoslavia 500,000,000,000 Dinar note for sale on eBay) and present day Zimbabwe, which has an annual inflation rate of nearly 2000 per cent right now.

As far as pegging currencies to USD - very few do that. El Salvador, Panama, Ecuador, Bermuda, the Bahamas, Hong Hong Kong, and China. In the case of China and Hong Kong, it puts China at a competitive advantage because they have their currency pegged artificially low, which makes Chinese goods cheaper in the US than they would be otherwise. In all those other cases, USD is simply the strongest currency in the region. In West and Central Africa, many countries have their currencies pegged to the Euro for the same reason. Worldwide, their are more currencies pegged to the Euro than any other currency.