is dried battery acid dangerous? more info in details?

Actually, there is no acid in an alkaline battery because it is.... alkaline. It has a zinc powder, potassium hydroxide (KOH) and manganese dioxide (MnO2). The potassium hydroxide can leak out (good picture in the link below). The brown substance you saw was probably because the leaking chemical reacted with the metal in the battery compartment.

Trace amounts of this will not hurt you. Both potassium and hydroxide are present in your body naturally. A large amount can hurt you, but simply washing it off with water will do make it harmless.

Large amounts of the material in a AAA could potentially be dangerous. But that small amount, as in that small of a battery, really isn't. The brown material you mentioned doesn't have the same characteristics as the acid in a car battery anyway. And it does wash off easily. You're good here.

I have the same problem with my piano keyboard and now there is brown all over the battery compartment.

I looked on youtube and they said you can clean white battery acid off with white vinegar and a cotton bud but there were no videos or any info on how to clean the brown stuff does anyone know??

They contain toxic materials but traces in the way you are describing are unlikely to cause you harm.

Its poison-es but since she washed her hands really well it means her no harm....^-^