Das means "the" in front of a noun and "that" as a demonstrative pronoun by itself. To mean "this" in front of a noun, use "dies". It can mean that baby but only the same way that the could mean that. It is not so specific. "Wir nehmen dieses Baby." "Wir nehmen jenes Baby."
That's not entirely true. "Das" can be a demonstrative determiner as well, so "we take that baby" is a correct translation. You are right that in written texts it is better to use "dieses" since you can't disambiguate between the article and the demonstrative determiner in text and thus it'll usually be interpreted as an article. But in spoken German you can make the distinction (by stressing the 'das') and it is common to use it as a demonstrative determiner.
It depends on context. If they both occur together in a sentence, often "dieses" will be translated to "this" and "das" to "that". But German doesn't really make the this/that distinction (unless you resort to "jenes" which is not used much anymore). So both "dieses" and "das" work as a translations of "this".
Can nehmen be used for both to take something from someone, as well as to take something to do something?
"We are taking the baby from you." "We are taking the baby to the park."