Shortest key in symmetric algorithm used only once is unsecured? Considering a message of n bits, one ridiculously short key of 1 bit and using this cryptographic function which performs the XOR operation to each bit of the message, resulting in a single ciphertext, could we assume that if the attacker doesn't know anything but this ciphertext, that this system is anywhere close to being safe?
If we don't know anything about the original n bit message, we can guess the message with probability $1/2^n$ which for anything but very small values of n quickly becomes zero. 
However if we xor the message with a single bit (repeating it n times) we only have 2 possible keys: 1 and 0. And the xor result is either the original message or it's negation. Therefor given a cipher text we have exactly two possibilities for plain text. And even if we know nothing about the plain text and can't validate our guess we can still guess with 50% chance of success. 

Guessing the plain-text with 50% likelyhood is not secure by any means. 

Obviously even with a very limited understanding of plain text, we would be able to determine which of the 2 options is correct.

Note security proofs for One-Time-Pad do not apply as we are repeating the key in the same message. This is no better than repeating it in later messages.