Will I be allowed back into the USA after one month?

Of course you can! Your ESTA clearance is good for 2 years. for multiple entries...as the site says. You may spend up to 6 months in the U.S. every year, but not more than 90 days at a time. You certainly may reenter the U.S. under the visa waiver program. Many people enter the U.S. under that program several times a year for visits of a few weeks up to 90 days. come visit with your friends and have a great time.