A really interesting 'Doctor X Tardis' fanfic I've come across is 'Tardis Tales'. In this fanfic, the Tardis has a sort of consciousness that the Doctor tries to fully understand. It delves into the mystery of the Tardis' inner workings and how it has a connection to the Doctor on a deeper level than just being a ship. It's a short but engaging read that will make you look at the Doctor - Tardis relationship in a new light.
Often, it involves exploring the unique bond and adventures between the human Tardis and the Doctor. There's a focus on how this unconventional setup changes their dynamic and the challenges they face together.
The Daleks could be the main villain. They might be trying to manipulate the Doctor's regeneration to create chaos in the time - space continuum. Since the 9th Doctor's unexpected jump to the 11th Doctor disrupts the normal flow, the Daleks could take advantage of this instability to further their evil plans of universal domination.
It could be the Daleks. They are a classic Doctor Who villain. They might see the meeting of two Doctors as a threat to their plans for universal domination and try to stop it.
Good character development in both the Doctor and the Tardis is key. If a fanfic delves into the Doctor's past experiences with the Tardis and how it has shaped him, and at the same time shows the Tardis evolving in some way, it's bound to be great. For instance, the Tardis could develop new functions based on the Doctor's needs over time. Also, a vivid description of the Tardis' interior and how it feels to be inside it can really make a fanfic stand out.
Well, it varies in different fanfics. The 11th Doctor could be hurt by powerful villains, or maybe in trying to save someone. It could also be from internal conflicts or emotional stress.