It would be best to apply an FDR correction, even if you can only use FDR < 0.25.
However, I see a lot of datasets that don't meet this criteria and have to proceed with using an unadjusted p-value. You should realize that you will may have a lot of false positives, but sometimes people can still discover interesting results that can be successfully validated with a different technology (which I would consider to be essential). I think the importance of the statistical rigor depends upon how much you focus on that data: if it is just going to be supporting evidence in a portion of one figure out of several figures covering a lot of non-genomic results, then you can probably get away with publishing an unadjusted p-value.
I'm not vary familiar with this particular tool, but I assume there is a CPM (count per million) table that you can extract at some point. You probably want to log transform your data prior to visualization, but that table can be used for most heatmap software.
Here are some commonly used functions:
http://www2.warwick.ac.uk/fac/sci/moac/people/students/peter_cock/r/heatmap/
If it is helpful to have a some sort of wrapper, you could use a table of untransformed CPM values as the input for sRAP (and you could also then see if you still get similar p-value and FDR values):
http://www.bioconductor.org/packages/release/bioc/html/sRAP.html
It was designed for RPKM values, but it should work with CPM values as well (I just don't know if the default rounding cutoff is optimal for miRNA-Seq data).
You should investigate why your data does not show change. Is the biological variability too high, or the data collection flawed, or perhaps the phenomena is unrelated to miRNA.
Otherwise you are just wasting your time and you will "discover" things that don't exist.
(also it is best if you ask one question at a time)
The variability may be high because I am using human samples. Also, as opposed to using a more focused approach on the specific target cell type, I am using whole tissue because there is a limitation to the cell isolation process. These are things I have at the back of my mind, and I will take them into consideration during my tedious validation process.
As with my other question. Is it possible to take results obtained from miRanalyzer to generate an output format that is suitable to be used by other software packages to generate a heat map?