Akershus is historically divided into the traditional districts of Follo and Romerike, which make up most of the county, with the exception of the enclave west of Oslo, consisting of Asker and Bærum, that was created after Aker municipality was transferred to Oslo in 1948.
Rental cars and taxis are often available, but are rather expensive in Norway in general. The public transportation system is relatively good with busses going between the major cities and stopping at buss-stops marked with a sign (blue with a white buss on it, rektangle) and/or an open air booth with the place name written above with white lettering. Public transport is reasonable though costs can build up if you buy tickets every time you get on, day/week/month/season passes can be purchased at the major stops and in any city at the central buss station, all the cashiers will speak english.
Norway has high water quality and tap water is completely safe. If you still want bottled water, most stores carry several brands of non-artifically treated water.
Most areas in Akershus are more or less crime free, and you should not be afraid to walk around alone day or night, though you should always take precationary messures and follow your common sense when in a new country. Signs and maps are all in Norwegian, but do not be afraid to ask for directions; the vast majority of Norwegians speak enough English to help out a lost tourist.