Sometimes, qvalue are smaller than uncorrected pvalues. Based on https://www.biostars.org/p/46187/
First, I think you are correct with being concerned about the estimated q-values and the presence of the warning. In my understanding, p-values adjusted for multiple testing should always be greater-equal to the unadjusted p-values. The warning also indicates that something in the estimation process went wrong. It might have to do with your p-values not fully covering the whole interval [0,1]. If the method tries to find an estimate for the percentage of true null-hypotheses in the data, due to the lack of p-values close or equal to 1, it might not be able to do so. At least this is my interpretation of the warning message.
A very nice manual is available here:
http://genomics.princeton.edu/storeylab/qvalue/manual.pdf
One of the expert replied to my email:
We usually let the qvalue package select the optimal lambda (see the 2002 pnas paper), as the optimal value minimizes the variance of the computed q-values around the estimated mean.
Other than that, a lower lambda value would mean pi0 estimates would be higher. lambda 0 would result in the conservative BH adjusted p-values. 
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