This brown algae sounds as if it is diatoms, this is fairly common in new tank set ups. Once the tank and filter has settled and the water column parameters have established a bit, the diatoms should naturally disperse on its own, this can take anything from a few weeks to a few months.
To answer your question regarding shrimps, yes, shrimps do eat algae but in such minutiae amounts, so shrimps as well as snails should not be relied upon to get rid of algae.
Generally speaking, the maintenance of your tank and algae control is really down to the fishkeeper responsible.