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I think the answer is not completely correct. The iOS support iAP/iAP2 which is similar to SPP.
The device should claim a specific 128 bits UUID in the EIR data and enable SPP, and then during inquiry, iOS will recognize the device and connect to device's SPP. However once both connected, there will be some MFi work to do for both to communicate over this SPP.
Q1. Does it the correct behavior that the BT SPP profile cannot be discovered and listed by the iOS device?
A: IOS doesn't support the SPP profile, please refer to the following link for IOS supported profiles(I can only find the Chinese version - auto connect to Chinese version in Apple's developer link with my pc, sorry for that): iOS：支持的蓝牙描述文件 - Apple 支持