Is it common to use "take it" in the sense of "assume" or "suppose"?
Using "take it" that way is common enough, yes. You could also say "I gather" as in "I gather you understand what I mean?" This could be posed as a question by one's tone of voice - a rise at the end for a yes-no question, hence the question mark. It doesn't have to be a question, however.
I would define "take it" to mean "interpret" or "understand in a certain way". It could mean "assume" or "suppose". An expression such as "take it that" can have shades of meaning depending on how it's used. This is a very fine point, however.
Is the word "reckon" common, too? I reckon that we'll have to leave early.
Yes, "reckon" is common enough, but I don't think it's used a lot in some parts of the USA. To me, it sounds western or southern. It sounds like a kind of "cowboy" expression. Outside of the USA, I think reckon might be more common in British English, but in Britain, it wouldn't sound like a "cowboy" expression. I think there might be something about this word in a usage note in the American Heritage Dictionary.
No, there's no usage note, but this might interest you: