I found this camera available for purchase as brand new for $450. Spending nearly $300 to repair an older version may no be a wise choice. You may find there is a market for the camera in its current non-working condition on eBay.
With that said, to your questions. 1) It will be difficult to diagnose without seeing it, but I have a suspicion in mind.
The viewfinder picture is actually what the lens sees, bounced up via mirror to a prism that projects the image to the viewfinder. If the mirror has become dislodged and is stuck in an odd position, the image would not be projected in the viewfinder. You can see the mirror when you remove the lens from the body. The mirror should be centered in the opening but at about a 45 degree angle. If it is loose or otherwise in the wrong place, this could be the problem. If the mirror is stuck and preventing the image in the lens from projecting on the sensor (behind the mirror) no capture will be possible. Other than the optics inside the lens and the mirror, there are few parts that could obstruct the image in the lens from reaching the viewfinder. Is the aperture of the lens open? If not, there may not be enough light to see the image in the viewfinder. This would also indicate that the lens is not opening up to let you see, and may not get set to the correct aperture when taking a picture. The camera usually opens the aperture to allow you to have a nice,
bright image in the viewfinder. When you press the shutter release, the
lens stops down to what the program says (or your manual selection) and
the mirror lifts up out of the way, and the shutter fires.
2) Can you fix it? Maybe. Again, without seeing it - its hard to know for sure what the problem is and I don't know your level of skill either.
My suggestion is to bypass the camera shop that "doesn't know what the problem is but will fix it for $270" (how is that even possible??) and deal directly with Olympus USA Service and Suppor
t by phone or email to get an estimate / factory trained tech perform the repair.