You are not allowed to separately program an AM station and its FM translator. The exception is if the translator is really simulcasting another FM station's HD 2, 3 or 4 signal. Then the translator cannot air programming separately from that HD signal. Since Kool Radio is not using the HD signal of any full power FM stations, the programming on the translator has to be the same as the local AM station.
Question 2... Why are 1270 and 1490 simulcasting? I suppose because the Tropical programming offered in Springfield makes more money than Oldies. So as they transition, they're keeping Tropical music playing on both stations during the construction work. You don't want the Hispanic population to get lost during that time. And again, if the FM translator MUST rebroadcast an AM station, and you have only one working studio, then you have to suspend Oldies so that the Tropical format is uninterrupted on the translator.
Now we might ask, does it really take a month to do this work? And suppose the work gets done faster? Maybe if the work is finished sooner than expected, they can restore Oldies on 1270 before May 1?