That's certainly a very specific set of issues
Regarding the 1st one, most of RPGMaker games only use the arrows, Z/Enter, X and Shift. In this case, Z/Enter is Accept/Enter, X is Back/Cancel and Shift is used for running.
For the saving it sounds pretty weird since I've had no issues regarding the method. You can check the folder where the game is to see if there's any savedata.
And for the crashing... Sounds to me a file got corrupted during the extraction or the RTP wasn't installed properly. You can check the RTP download in the 1st post, right below the "Download" links.
I'd suggest a clean install of both the RTP and the game (I know it doesn't install, but I mean to delete it and extract it again). It most likely will solve the saving issue too.