What is a Reacto Tester unit and are there any projects in which I can use it?
A TV repairs man would use a unit like this to find out if the electron guns in the cathode ray tube are still sufficiently emitting electrons. CRT's wear out over time and the picture vanishes over years of use. It is pretty much a pass/fail test: if the CRT is OK, you can repair the TV by adjusting the voltages on the circuit board. If the CRT is not OK, ... you scrap the unit.

EDIT: As @david explains the REJUV setting can be used to rejuvinate or 'clean' the filament in a CRT, after using that on a worn out tube, chances are that the picture gets a bit brighter again, but the solution is only temporary and the filament may burn out all together. 

To answer your question about if these units are still in use today, look around you and count the number of CRT's you see. If you find any, chances are that replacing them with a modern TFT screen is cheaper than getting the old one repaired. Apart from that the later models of tubes are probably not supported anyway.

As for age? Don't know. Value? Don't know, maybe collecter's value. Should you toss it away? In my opinion this sort of stuff deserves a collector.