Abortion (within a certain time frame) is not murder.

OBSERVATIONS:
"I think abortion should not be considered murder (ethically), if it is done before the first two months of a pregnancy."

~ Murder and ethical are mutually exclusive terms and should never be used together. There is nothing ethical or unethical about 'murder.'

"However, I firmly believe that when the fetus first develops, it is just a clump of cells. The reason I don't consider it to be a new living organism is because at this stage, the baby (fetus) cannot yet feel, or think, but most prominently suffer, and counting the destruction of cells as murder compared to the murder of a person or pet (who can feel senses) is simply not ethical."

~ This right here demonstrates your lack of education on the subject material.
Clump of cells? Not a living organism?
The baby (fetus)...?
Bringing a pet into this also shows a measure of ignorance too.

Scientifically, at conception, the very basic biological criteria for "life" are met; therefore, it is alive/living but it is clearly NOT [a] human being (ie - 'a person'). It has potential to be, but it actually is not. Potentiality =/= Actuality. Also, a fetus =/= [a] baby either. That term, baby, is a misnomer, an appeal to emotion fallacy.

""If it's consciousness that you care about, would you kill a man in a coma?" I really don't have a good answer for this..."

~ You should, and it is easy. That argument is a false equivalency fallacy. One cannot compare a pregnancy to a born human being, regardless of their state (e.g. coma, under anesthesia, asleep, etc.). Why? Simple. The pregnancy has NO legal rights, privileges, and/or equal protections of the law - unlike those born who do (14th Amendment; 1 USC 8).

" What if it was a brain-dead man? I personally believe it is fine to pull the plug on a brain-dead man, although it should be done with consent from close friends or family. In this state, the man has practically turned back into a fetus that is incapable of living by itself (in fact, one who is brain-dead is legally considered, "already dead")."

~ This is nonsensical and utterly irrelevant to the debate topic. And the "the man has practically turned back into a fetus..." Incredibly ignorant statement. Think before you type. If it sounds uneducated, don't post it.