Translation:I am busy for a little while.
"(something)間に" marks a specific timeframe in which something occurs. For example: 5日間に = "within 5 days" (and no more than that), or 留守の間に = "while I am/was out" (thus before I return(ed)). This sentence on the other hand leaves it somewhat vague how long 'a little while' actually is.
It is a awkward translation, ceo to secretary: I'm going to be rather busy for a bit.. Hold my calls. I'm a bit busy right now.. A little busy.... For a time.. For a short time.. For quite some time.. For quite awhile? I dunno quite how i might improve it... How long is awhile? A little bit of time.. A brief time... Some time.. A little busy so.. Maybe, "I'm a little busy at the moment.? Hmm
I think that 時間 is the counter for hours, so, if it was 時間, it would mean "a few hours" instead of "a little time". To your second question, I don't think it is, since it could mean "a little space/distance" as well. But I'm also learning and these are just my impressions.
This is absolutely incorrect English. "I have been busy for a little while" - OK. "I will be busy for a little while", maybe bets is: "I am busy recently". But you can't imply progression with "a little while" and use simple present tense at the same time. I suppose it's like a Japanese high school test of English. You have to learn incorrect translations to pass! I will memorize this incorrect translation for next time.