Will spaying female cat make her nicer?
It may help to spay her, it sometimes calms them down - I doubt it would make it worse. It is worth it - and not just for the obvious reasons, not spaying a female cat can lead to uterine and mammory cancers. Whenever she scratches or nips, spray her with water.. keep the water bottles on hand all the time. And when she is playing nicely with her toys reward her with a treat. If it does not calm down after you have her spayed, or after consistently trying the water and reward method - or others in these responses (one good whap may actually help in this case - she needs to know it is wrong) - take her to the vet and speak to the vet about whether it could be neurological. Prescriptions drugs may work for her. Otherwise you should try to find a home that can safely have her.
How can I make her trust me again?
It's very difficult to get back broken trust but still it's possible. These are few waysDon't do any show off to please her as it will only worsen the impression.Be honest and truthful. It will take time but it's the best healer which work on broken relationship.Just be yourself.Don't regret for your act but take the lesson from it and forget it.Whenever you find right time , place and mood you you can apologise once. Not more than that.Wait for right time . It heals the things automatically.When you lied her she must have felt bad .That feelings remained in her eventhough she forgave you for some reason which was not in actual. Forgiveness is not possible by keeping any impression of painful feelings within.What changes you are experiencing is because that feeling is emerging out in the form of such behaviour. You should accept it without creating any more painful feeling from your side to stop the exchange of it from both the sides again and again.You need to accept it in happy manner consideringit the outcome of your lie. As happiness and taking self responsibility of it will help you to check to produce such painful feeling which means this chain will break very soon.