One way to take it is that Tyrell is Elliot's dad, except younger than the Christian Slater version, like when he worked at Evil Corps. Joanna discusses giving birth to a girl and giving her up for adoption while talking about how much she loves her newborn son. This could refer to Darlene, and how she is absent from all of Elliot's childhood flashbacks. She also looks like Elliot's abusive mother. She seems to know Elliot when they talk, and looks like she may know about Elliot's mental illness, similar to Elliot's mother later in the finale in Time Square. Is Tyrell another manifestation of Mr. Robot? Possibly. Another way to take it is that they are all real people, just another couple repeating Elliot's childhood memories.
I hacked the serie and I am leaking all this information:
Elliot's dad was a drunken person after his mr robot bussines went bankrupt. That explains why he is pictured like that since the beggining. He was beating Elliots mother or something until one day Elliot fights his father and throws him through the window. After that Elliot started blaming himself and his mother also blame him undirectly. He starts having mental dissorders but in the future becomes an IT guy... a lot better than his father. He joins E-corp and becomes what the representation of Tyrell is. He is a very succesfull married IT young guy who wants to become the CTO at E corp. After he doesn't achieve that, he starts having dementia and Dissociative identity disorder. Mixing his old past (as Mr robot), his past (as Elliot) and his present (As Tyrell). *Tyrell speaks swedish because danish is way too difficult to learn... Just a joke :P