Difference between a 3 phase VFD inverter and UPS inverter
a- Does A UPS system uses feedback from the output voltage to correct the PWM , to compensate for battery draining, or does it use fixed values since the waveform is constant (no voltage control)?


Only extremely basic, fixed-load SMPS can work without feedback.

So, yes, your UPS certainly has a feedback. That might be a direct voltage feedback, or indirect – for example through a magnetic flux measurement through a tertiary winding through a flyback transformer.

For details, you'd have to refer to the specific architecture of your UPS.


  Does A UPS system use current control ? In a VFD you can Limit the motor current using V/hz or FOC , and reduce supply voltage , but can that might not be applicable in UPS .


See above. A UPS is not like a motor control in that it's job is to supply a defined voltage (not a defined current), so current feedback is at most an indirect way of determining the state of the system.

Certainly, there will be measures to protect against overcurrent. But that's much like saying a fuse is a current-controlled device.


  b- How does a UPS react to an overload typically ? ( turn off or limit output ).


Depends?

Limit output is marketing talk for "I'm not able to get enough energy together to generate the voltage I should be generating, so I'm just trying my best". So, yeah, to some degree, as every supply that is not extremely oversized has to react to load changes, every UPS will drop a bit in voltage when the current draw suddenly increases. 

But: it's a UPS. If you're driving it harder than it's designed to be driven, it's definitely a user fault, and it would be square and fair, and probably safer, to just turn off. But: that depends on what your UPS is for. You'd probably let a UPS for a data center just shut down single circuits if it detects overcurrent on these, whereas a hospital UPS might have different design goals.