Have a look on this forum for Kolban's book -in announcements recently- and maybe look through there . There is a wealth of info in there to absorb.
I suspect it's to do with your serial terminal setup . In 115200 baud you are typing the command followed by a CR and LF so it should be getting there .
if I set the baud to 115200 and send "AT", I get back garbage. If I set it to 9600, I get back "AT". If it was shorted, I'd get back what I sent regardless of the baud, correct?You said this earlier . You should get back "OK" when you send the AT command on 115200 .
They say some modules work on other baud rates but I have not had one of those.
I would suggest you get another module if you can and do the same to see if that works OK with what you are doing then you will know if it is you or the module. If the original one is toast then you have to get another anyway .