How old is that?? Late 1980s?
We got several Philips/Fluke PM3320, PM3323 and PM3340 scopes back in 1988/1989 shortly after they had been introduced.
I liked them a lot, they were easy to operate, reacted quickly to user input (and offered a numerical keypad!), and proved to be extremely reliable. PM3320 and PM3323 quickly became my day to day scopes back then. At least until the faster HP 545xx Series came out
Can't this scope be used as a general purpose oscilloscope in the lower bandwidth range?
To some very limited extend only, and even then it's a very poor general purpose scope because of its timebase limitation, the 50ohms only inputs, and because it's no real-time scope. As others already stated it's a sampling scope made for RF analysis (primarily eye diagrams), something which back then was not possible to do with real-time scopes because their sample rate was too limited.
These days the scope and its technology have long been obsolete. 2GHz real-time scopes have been available since the end of the '90s.
Does it provide sampling memory? How many seconds can be sampled at given bandwidth?
The PM3340 (as the PM3320 and PM3323) has four separate sample memories of 4kpts each which means you can store four different waveforms.
As a bonus, the PM3320/PM3323/PM3340 are 10bit scopes.
How is the FFT functionality?
Very slow, and really very basic. FFT was an option on PM3320 and PM3323 (if I remember right it came standard on the PM3340), and if my memory serves me right it used some 500 points or so. Back then that was great. 27 years later it simply isn't.
Can it act as a basic spectrum analyzer up to 2 GHz?
Not really. FFT in those scopes was meant to look at the frequency components of a repetitive signal, and the (by today's standards) painfully slow processor and the low memory present severe limitations to its performance.
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