What should be the slit separation d in terms of wavelength such that the first minima occurs directly in front of the slit s1?
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You are confusing interference with diffraction. Distance between fringes depends on the distance between slits only. So, when you keep the slit distance constant and change their widths, the distance between fringes stays constant, and the number of them visible depends on the size of the part of the screen that is lit. And this increases with increasing diffraction, i.e. with decreasing slit width. Oh, and the slit width can't really be "much wider than the wavelength of light", because the distance of them wouldn't be comparable to the wavelength, and you'd get no interference pattern at all.
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