It's important to note that birds take a lot of time to get bonded to you, one of my lovebird took A VERY LONG time (nearly 3 months) to be tamed.
Here's what you can do-
Take treats in your hand and give your bird the treat, like when you have to give your bird when it is in the cage, don't put it into your palm, it's scary for inexperienced or new birbs. Give it using two fingers, just like you hold a needle. Your bird may be scared at first, but he or she will come around.
After your bird is comfortable taking treats out of your hand when you give it using two fingers, now you can put treats ON your index and middle finger and offer your hand to the bird, now your hand is horizontal, you aren't HOLDING the treat, you have just put the treat on your hand. While before you were holding the treat.
After that you can start to unfold one finger at a time... and slowly, slowly. All your fingers will be unfolded (REMEMBER TO ONLY PUT THE TREAT AT THE CORNER/EDGE OF YOUR FINGERS)
Then you can just start to move the treat backwards, towards your palm and within days, your bird should be eating it out of your hand.
Keep in mind that this process can take from a week to a month. So be patient
When it comes to teaching your bird to step up onto your hand, just take a treat and put it near your finger (make sure your finger is horizontally positioned so that it looks like a perch) your bird will resist but keep trying. At first whenever he/she keeps one of his feet on your finger give him the treat, later try encouraging him to keep both his feet and double the reward (like if you were giving him/her 1 wheat berry on keeping his one foot, now give him/her 2 wheat berries for keeping both the feet.)
Again, this process can take from weeks to months... I hope your bird comes around to this idea soon.
I don't have a lot to say about the food tray one, is the food tray made of wood?
If yes, then he may be biting it because he likes to shred wood. Make sure he has enough wooden toys to satisfy his crave, but sometimes, birds just prefer one thing over the other!
If the food tray is made of plastic, then you need to remove it immediately and put his food into another bowl (stainless steel preferably)