Greetings all!

I am new to microcontrollers. I was hoping you kind folks could help me out with a few questions. First, however, please correct me if any of the following are wrong.

1) If a program is small enough for a given processor, you may end up needing neither external memory, nor an OS, nor any other software routines that are not your program.

2) External memory, if added will always slow a program down, as would an OS or any other software routines not necessary for the program's task.

3) Microprocessors require external memory.

Now for my questions.

I. If I want to write a small number crunching program, say 58K, that can fit into an 8051's ROM, but requires as much speed as possible, can this program not be written for a microprocessor also w/o an OS?

II. If so, where can I get tips on writing routines to figure the accurate speeds of running the program on a system developed with a microcontroller versus running under a system developed with any given microprocessor? (This means taking all the processing time into account, including accessing external memory for microprocessors.)

III. Can software simulators run programs at the same speed a chip would run them at? Or does the simulators running speed depend on the desktop speed?

Thank you for your time.

-Freddie