Is it ok to use an old phone as an universal battery charger?
I would strongly recommend against that. Some charging circuits are designed to charge a battery at a specified current. That current is chosen to be as high as possible without risking damage to the battery. If you try to charge a different battery at that current, a battery which may not be able to handle that much current, there's at least some chance it will heat up and start a fire.

In general, I wouldn't mess with Li-ion batteries unless you're very sure about the specs of both the battery and the charger. And even then, I'd be careful.