This is rather simple. According to Grammar Girl, each other is always two words in English. The AP Stylebook further explains each other and one another, where more confusion occurs.
As quoted from the 2007 AP Stylebook “Two people look at each other. More than two look at one another. Either phrase may be used when the number is indefinite: We help each other. We help one another.”
To sum it up, eachother is not a word in English. Each other and one another depend on the number of people involved.
For some reason I’ve been having trouble with when to use who and when to use that lately. I used to have it down, but just like the one time in high school I wrote an entire paper without using than (I had convinced myself it wasn’t a word…), I’ve gotten myself mixed up.
Luckily for me a quick Google search helped me remember what I already knew and cleared away the confusion.
The simple answer is Who is for people. That is for objects.
The more complicated answer is addressed by my favorite Grammarian, Grammar Girl (post can be found here). She found that according to the Heritage Dictionary, “It is entirely acceptable to write either the man that wanted to talk to you, or the man who wanted to talk to you.”
Grammar Girl determined it is a bit of a grey area. “My guess is that most people who use who and that interchangeably do it because they don’t know the difference,” she wrote. “To me, using that when you are talking about a person makes them seem less than human.”
Something else I learned in her post, “whose, which is the possessive form of who, to refer to both people and things because English doesn’t have a possessive form of that. it’s fine to say, ‘The desk whose top is cluttered with grammar books,’ even though it is obviously ridiculous to say, ‘The desk who is made of cherry wood.’” I didn’t know that!
Bottom line: who is for people. That is for objects.