If I will be applying for naturalization, is it alright to travel in the time out of state or even out of the country in the time period before applying and waiting for the result?

Yes, you may travel. However, you must remember that you will have 3 appointments. Your biometrics, the interview and the oath. Any delays of these will delay your approval. In addition, you must maintain all your qualifications until you are sworn in as a citizen. Thus, if you any of your trips outside the U.S. break your residency, you may disqualify yourself. This will depend on how long you go and how many days you have already spent outside the U.S. Thanks. Harun@ksvisalaw.com