First, I recommend you remove the mirrors from the budgies' cage. Mirrors are not a good choice of "toy" for birds. Budgies can become obsessed with their reflection and it can cause aggressive and/or territorial behavior. Additionally, some budgies will regurgitate to their image to the point where they become malnourished. In the one picture, it appears that Ozzie is more interested in the mirror than she is in Pepper which gives you an indication of a potential problem...
With regard to Ozzie and Pepper -- you need to give them time and space to get used to the changes they've both been through.
Pepper is young and wants to be friend but Ozzie is an older bird and it may well take her some time to warm up to him.
Not all budgies become "best buddies". The fact that Ozzie is tolerating Pepper and has allowed him to sit next to her a couple of times is a good sign.
Keep in mind that budgies pick up on human's emotional state so you need to be calm and relaxed whenever you are around them and interacting with them.
Give them time and let things play out. There is a good chance that even if they aren't "best friends" having a housemate will be beneficial for Ozzie in the long run.
Is Ruby in the same cage with Ozzie and Pepper?