One common theme is the journey of their relationship, like how they first meet and gradually fall in love. Another could be overcoming obstacles together, such as dealing with family or work - related issues.
The significance might be that she is a central figure in the memories associated with the cemetery. She could be the one who imparts important life lessons to Emily in that setting.
Emily's mom had a special connection to the cemetery. She might have been a gardener there, tending to the flowers around the tombstones. Emily grew up seeing her mom's love for that place. After her mom passed away, Emily would often go to the cemetery to feel close to her again. She remembered how her mom would talk to the stones as if the people beneath them could hear. It was a strange but beautiful relationship her mom had with that cemetery.
Sure. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for 'andy x emily' there, and you'll find a variety of stories written by different authors with different takes on their relationship.
The story behind Opie's mom is somewhat mysterious. It's never fully explored in detail. It seems she had her own reasons for leaving that were never fully disclosed in the show.