Q: The IMA light, battery lighy, and check engine light all came on and the AC stopped blowing cold all at the same time

The IMA (Integrate Motor Assist) light relates to the Hybrid function of your vehicle, specifically the Hybrid battery pack. This light indicates that the battery pack may not be charging to its full capacity anymore. This is likely also the reason your check engine light is on. Code P1600 relates to faulty ECM battery function or poor connection, which is a result of the battery pack not charging. Code P1570 indicates a poor voltage problem, which is also a result of the poor battery charging. I would suggest taking the vehicle to your local Honda dealer to find out what options may be available for your battery in terms of any warranties or replacing it.