*** You cannot use the Brainwallet BIN to HEX converter due to the fact that Brianwallet adds a 0 place holder to every 4 bit BIN sequence. e.g. 1111 converted to HEX is F but Brainwallet converts it as 0F ***
Yes, you can. Just don't add spaces to the binary.
Also, don't use random.org at all. Use a physical coin, or a known-good physical RNG, preferably one that is designed to be unbiased, truly random using physical noise, and separate from a computer.