when was it opened for public?
1908
PATH (rail system)
The system began operations in 1908 and was fully built out in 1911. 
where does the path train from hoboken stop Lower and Midtown Manhattan in New York City
wiki:12091513
PATH (rail system) [SEP] Introduction
It operates as a deep-level subway in Manhattan and the Jersey City/Hoboken riverfront; from Grove Street in Jersey City to Newark, trains run in open cuts, at grade level, and on elevated track. The routes of the PATH system were originally operated by the Hudson & Manhattan Railroad (H&M), built to link New Jersey's Hudson Waterfront with New York City. The system began operations in 1908 and was fully built out in 1911. Three stations have since closed; two others were re-located after a re-alignment of the western terminus. From the 1920s, the rise of automobile travel and the concurrent construction of bridges and tunnels across the river sent the H&M into a financial decline from which it never recovered, and it was forced into bankruptcy in 1954.