Seems simple enough, and it is obviously ASCII based. Yes, you will have to try everything twice - once with null modem, once without until you get a reaction - it isn't clear if it is DTE or DCE, so best to try with and without until something happens!
Don't think its wise to attempt to type the commands, there could be timing requirements. Try creating a text file with the correct commands (make sure you follow the upper case specified in the manual, just in case!) then pipe this to the serial port either from the command line or from Hyperterm. Be concious that your PC will probably add <cr><lf> at the end and the projector might not like that, and yes, you will definitely need the [], looks like it uses this to parse/as delimiters....