Is it possible to write direct machine language instructions to the processor and have them executed in some manner?

Technically, Yes you can... Will most people tell you how, No...
Just either, write a PE file in Hex by hand, or just use the mnemonics as most normal people do... The only reason I see one would want to do that is virii coding.. Now, if you want a user to write mov, eax, 1 in an edit box and have the processor execute that, then you will have to write/use a scripting language or something...