The engine serial number, if that is what you are seeking, is on the left (drivers side) rear of the engine on a flat surface at the top of what appears to be the block. As for the number in the V.I.N, it is the 6th number. Should be a "6" since no other engine was offered.
It should be the same exact thing
Knock sensor/vibration sensor
Not necessarily.
Yes, at the age of this vehicle you probably should.
The 2001 Subaru Forester has a flat 4 engine.
The 2004 Subaru Forester has a flat 4 engine.
The 2013 Subaru Forester has a flat 4 engine.
The 2012 Subaru Forester has a flat 4 engine.
The 2002 Subaru Forester has a flat 4 engine.
The 2010 Subaru Forester has a flat 4 engine.
The 2006 Subaru Forester has a flat 4 engine.
The 2005 Subaru Forester has a flat 4 engine.