Not sure if you are going to address this question to Awneil, hope you don’t mind I add my comments below.
For problem mentioned, can you share which FW is running on your Q2687 module? Are you able to test using latest FW, e.g. R7.46?
For (3), normally as soon as “+CMGS: xx” received from module, you can send the next SMS. For test and play safe, you may add 2-3sec delay but not necessary.
For (4), I am not sure the actual improvement as the time depends also on network, but you may try:
i) use flash as SMS storage (AT+CPMS=“ME”,“ME”,“ME”)
ii) use GPRS or circuit switch, AT+CGSMS=2 or AT+CGSMS=3
Thanks for your inputs/suggestions; There is no code inside the module; we are using it as standalone unit @ for PC application software to send/Receive alerts SMS based on some predefined Conditions.