Well, on my old SYM-1 BASIC took 8K (no graphics, and a few hundred bytes needs to be added if full trigonometric functions were required). The Assembler/Editor (you need an Editor as well
) called RAE requires 8K again. But there are smaller solutions around here.
The disassembler is something, I recommend to do by yourself! It is not very difficult to write such a program if you start with BASIC (you can use PEEK(address) to step through your source program). This will greatly help to understand everything. Written in assembler a disassembler might be as small as 1/2K, but 3/4K or 1K is pretty easy to schieve. Of course, this will be a primitive one, not as sophisticated as White Flames' one.
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A single screen where one can select amongst these options. Not really an OS, just a single menu.
Your monitor could print a banner with that contents. Then you "select" one, say starting BASIC. When you finish BASIC you return to the monitor loop where the banner is reprinted.
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A version of BASIC good enough for my young son to enjoy.
This could be a problem. You didn´t say anything about your display. A "dumb" terminal might be something your son wouldn´t enjoy that much..
You should also take some thoughts about saving/restoring information/data to/from your machine. This may have an enormous impact to and how all other software will and can operate.