Hi, I am under f1 status. I am planning on taking a semester abroad and I don't want my absence to be for more than 5 months. Since I'm not coming back until next spring, my I 20 will be terminated in Sep. but can I still enter the US during August, while my I 20 is still valid?

Have the school endorsed I-20 to make sure before you leave. If you return with one month validity on I-20, you may not be able to return.