I think this may be a duplicate question submission -- Your conditional residency means that USCIS has forgiven your past overstay. You should not have problems re-entering the US, assuming that you don't stay abroad too long. Good Luck
It is confusing as to if you are on tourist visa, or if you have a green card. If you have a green card, even a conditional one, then your past overstay is not an issue and you can travel abroad safely for up to six months. If you do not have a green card, you need to be very careful as you will likely be subject to a 10 year bar on reentering the US. If you are still confused, talk to an immigration attorney.
Yes you can go home for a month with the conditional green card. Bear in mind that you cannot be out of the U.S. for 6 months or more at a time.
For more detailed information, you may contact an experienced immigration lawyer at Bogle & Chang law firm to confidentially discuss the case and how we can help. We handle immigration cases in all 50 states. Our law firm information is provided below.
Good luck to you.
Nikiki T. Bogle, Esq
Immigration Legal Team
Bogle & Chang, LLC
Phone: (800) 342-1733 ext. 101
National Immigration Lawyers
We handle immigration cases in all 50 states and foreign countries worldwide.