IMHO:
1). Maybe, but used test equipment is like used audio equipment, it may need repair, it may need calibration, or both. DIY with new, quality components can be very cost effective and satisfying. I built my own signal generator that provides the sine, square and triangular waves. It uses signal generator chip that I built the circuit around. The sine looked clean last time I used it, but it has been a while. You can also get a software package and use a smartphone or computer. That is my next signal source I am going to try on my SX-1050.
2). Use a scope, distortion analyzer, and maybe a frequency counter.
The only way to be sure is buy new with a warranty, but that, of course, means $$ or cheap far east stuff with poor customer service.
Wish I had better answers, I have the same issues. I bought a portable multimeter a while back, and discovered after I got it it was missing the ac voltage range most useful in audio repair. Autorange, and I knew better than to buy an autorange but . . . I ended up using the temperature probe on output transistors more than anything.