Brown algae is usually diatoms. They feed on excess silicates so you may want to test your water for it to see if that't why you have them. If the tank was recently set up the diatoms will eat up the sillicates and then dissapear on their own, 1 week to 3 months after setup.
Ghost shrimp are not diatom eaters. They really only eat uneaten fish food and dead animals. Cherry shrimp are largley biofilm eaters, eating the nutrient dense film full of critters that grow on rocks, driftwood, and decorations. I do believe they eat diatoms, but not off the glass.
Snails are your best friend for getting rid of diatoms. Ramshorn snails are busy little guys and won't overpopulate a tank unless you overfeed. They're easy to spot and remove by hand when you want to get rid of them or reduce their numbers as well, and their babies make delicious live foods for hungry fish. :)