Thai currency is called the Baht. And for those who do not read or understand the Thai language, denominations are written in both Thai and Western numerals on their currency. 

Thailand does not limit the amount of dollars or western currency you bring into their country. However, bringing in more than $20,000US  must be registered with Thai Customs.  They DO limit the amount of Baht you can take with you once you leave. 

Note that many countries have a $10,000US  threshold wherein you cannot move more than that amount from one country to another without a written authorization.  Be prudent and do the majority of your purchases with your ATM card, and leave the western currency at home until you plan to make a large purchase.  Then do the transfer.

Holding a valid Work Permit or a House Registration Book (see Visas) should guarantee that you can open an account at a bank.  But if you plan to stay just a few months at a time, you CAN find a bank that will welcome your funds. All it takes is presenting a passport, your Non-Immigrant Visa and a credit card that is tied to whatever bank you use in your native country.  You may have to visit several banks before you get one to agree to open an account for you, but keep trying.  One bank WILL help you out!

Most currencies from outside Thailand are accepted for deposit at Thai banks.  It will be put into a savings account, not a checking account, however.  There will be a conversion charge as well.

Banks in Thailand do not pay interest on your deposits, or if they do, the interest rate is extremely low.
 
Banks that have been known to open accounts for holders of a Non-Immigrant Visa are: Kasikom Bank,  Bangkok Bank and Siam Commercial Bank.