If I say: 'she is a forgiving person' but in the context that she is a person who screw up times to times but has a nice personality and that she should be forgiven, would that be correct? or at leat undestandable given the context?
No, that would not carry the meaning you want. Your intention would not be understandable.
A "forgiving person" is a person who forgives, not one who is themselves forgiven.
You could say:
- She deserves forgiveness.
- She is worthy of forgiveness.
- She deserves to be forgiven.
- She ought to be forgiven.
- She should get a second chance.