MicroRna's are very short sequences, on average just 22 bases. That is even shorter than the already short length of an individual Affymetrix probe, and you do not have the whole probeset to average out. Since miRNA sequences can be very different in base composition and thus in binding strength (often denoted by the melting temperature) the fractional binding for individual miRNA's would be very different. To prevent that it helps if the reporters on the array are thermodynamically stabilized. I.e. they are chemically modified in such a way that every individual base pair has the same binding energy. We had good experiences with Exiqon arrays that use this approach.

Yes, Affymetrix even has special miRNA chips designed specifically for this purpose: http://www.affymetrix.com/estore/browse/products.jsp?productId=131473

I would guess that some of their competitors have similar products, but I have not checked.

There are indeed miRNA arrays commercially available, from Affymetrix, Agilent, Illumina (although I have never used the latter) and probably others.

Yes, you have GeneChip miRNA arrays from affeymetrix, they are constantly updating with the miRBase versions. You can use this.