How does one translate these sentences? "Jim has as little food as Sam." or They've got as little water as we have." or "We'll return your file in as little as 12 hours." This comparative construction is opposite of 'as much as'

I don't think we should talk 'opposites' here. As little as (no more than, not over, within), or as much as (however much) are used in different ways.  And they are also different from when comparing quantities.
1.
I'll be back in as little as 2 hours.
M'ap tounen nan dezèdtan.

2.
You can buy a radio for as little as five bucks.
Ou kapab achte yon radyo pou pa plis pase senk dola.

3.
This song is so easy, kids as little as five can play it on a guitar.
Chante sa a tèlman fasil, timoun ki gen pa plis pase senkan kapab jwe li sou yon gita.


And using as much as, in that sense:

4.
You can eat as much as you want.
Ou kapab manje mezi w vle.

5. 
As much as we don't want to admit it, there seems to be no hope for the country.
Malgre  nou pa vle admèt sa, sanble pa gen espwa pou peyi a.
   
6.
As much as I want to help you, my hands are tied.
Malgre jan m ta vle ede w, men m mare.

And using these for comparing quantities, I would say:

as much as, as little as → menm mezi, menm valè, menm fòs, menm kantite, menm, menm ak, 
7.
Jim has as little food as Sam.
Jim gen menm valè manje ak Sam

8.
They have as little water as we have.
Yo gen menm mezi dlo avè nou.

9. 
I have as little food as you do, so I can't share mine with you.
M gen menm fòs manje avè w, kidonk m pa ka pataje pa'm nan avè w.

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