Ok one you need to be more patient. You've not been doing it long enough yet! Also lovebirds are naturally territorial about the cage so you will be limited to how good that's going to get. You are seeing progress here but like we all said to you it takes many months, sometimes longer and you must be patient.
Also if he nipping you its because YOU are doing something wrong.
Your movements are too fast or sudden for the bird
Lovebirds are naturally this way about their cage so you will not change that, its something that can be reduced but it will not disappear completely. My cockatiels still do it, its just natural for them and you have to accomodate that.
You are reacting to bites, if you pull away suddenly, or say owww or panic, this makes the bird do it again and again to you musn't react.
The bird doesn't have a good routine- your bird needs to have 10-12 hours sleep every night and to have good foods as this can greatly affect behaviour
The bird needs more time outside the cage, the bird is becoming aggressive because its stuck in the cage for too long every day.
There's nothing wrong with your bird just something from the above or a mixture of things. Its really nothing to get stressed or sad about. In fact all that will do is make it worse. Be patient with your bird, its hard for him to learn al he is doing and he's doing well. Hands are wayyyyy into the future, you can't do target training for 2-3 months and suddenly expect him to be OK with hands, that's not how it works.
Also with petting, some birds just don't like to be pet... ever. The will be tame eventually, sit on your shoulder or finger and play but they just don't like it sometimes. Not everyone wants to be cuddled right? Its the same thing.
If you bought a bird just for that reason, to pet and relax with it then I'm sorry but that isn't always how it works out. You should have a bird for more reasons than just that, not just entertainment for you. Its not something you can command to do what you want, its a living thing with its own mind.
You just need to slow down, stop being impatient and accept progress when it comes. If this stresses you this much what will happen during the birds sexual maturity or when it starts screaming (can happen during molting and breeding season) or if it gets sick. Now THAT is mildly stressful

This is just the reality of training a bird and is normal- just got to get on with it and be patient.