To take...
For me, this one always uses "a".
To take a vacation.
However, if you change it to a noun (gerund) it can lose the "a":
Taking vacations is my favorite past-time.
I speak American English, so, it may be that "to take vacation" doesn't sound wrong to British English speakers.
To go on...
Both with and without "a" sound fine, but possibly with a small difference.
I went on a vacation last week. Where did you go?
I went on vacation last week. Oh, that explains why you weren't in the office.
To me, "to go on a vacation" seems more exciting than without a. I would use the second version, if I do not intend to tell people where I went, but rather, just want to tell them I was gone (although they might still ask anyway).
The perspective is a little different.
I went on a vacation to Italy. (the place you went to)
I went on vacation from work. (the place you left)
But you could also say,
I went on vacation to the Bahamas.
To be on...
Same as To go on..., the article just changes the emphasis a bit.
Hello, this is XYZ Management Services. How can I help you?
Could you transfer me to Susan?
I'm sorry, she's on vacation till next week, do you need help with your account?
Both are fine and seem to be widely used. To me, "don't have the time" implies a long-term situation, whereas "don't have time" could be more temporary. For example, "My life is so busy that I don't have the time to cook" versus "Tonight I'm going to a concert so I won't have time to cook."
Best Answer
Means more than one cat is able to drink milk.
as written is not grammatical in normal usage, because a singular noun needs an article. So it should be:
The only difference is the number of cats involved.