what the best E-value cutoff in the miRNA homology search
If you are using BLAST for short nucleotide searches then you should reduce your word size to &lt;=7. It is better to align with mature sequences.

E-value depends on the database size. If your target database is huge then you should increase the e-value cutoff. If miRBase (for a few organisms) is your database then there is no need to run BLAST, also. You can simply run SSEARCH (Smith-Waterman Local alignment algorithm). 

If you are running BLAST against miRbase you can set the e-value cutoff at 10. This is fine because there are many similar looking miRNAs with different function. If you reduce the e-value cutoff then you may lose these. 

There are some other criteria for miRNA conservation- e.g there should be very high (almost exact) similarity at the seed region. After the BLAST, make sure that seed region is conserved.


  Can we can use DAVID for miRNA functional analysis.


I don't think DAVID can be directly used (miRNAs have to be annotated in their database). What you can do is that you can predict the targets of your miRNA and then pass them to DAVID. DAVID won't do the predictions but there are other programs (see this post). You can also try BioMart (provided by ENSEMBL) for getting GO details. Even BioMart does not provide functional annotation for miRNAs (I just tried, to verify). So best thing is to check for the targets.