A brief answer on a large subject: The fastest film I'm aware of is Fuji Superia 1600, a colour negative film that is also sold in other flavours, such as Natura 1600.
There are two B&W films with a faster speed on the box: Ilford Delta 3200 and Kodak T-max P3200. These are both usable at EI 3200 and 6400 (depending on your quality requirements, in particular the amount of shadow detail you want) but they aren't true ISO 3200 films. The manufacturers rate them at ISO 800 to 1000. The ISO is the film speed obtained by standard methods. An EI (exposure index) is just a practical rating on the same scale as ISO speeds.
You can push other films like Kodak Tri-X to high speeds, but the quality deteriorates the more you push. You don't gain much true speed by pushing.
The Rollei R3 film is about ISO 400. I have used about thirty or forty rolls of it, but haven't tried it beyond 800.
Superia 1600 is said to be ISO 1600 by Fuji. I'm happy to use it at 1600, but shadow detail is marginally acceptable. I've never tried to push it. I prefer to push one of the ISO 800 films. The current version of Portra 800 is my preferred colour neg film for pushing at the moment. For two-stop push processing I set my meter to 2000 for Portra 800.
Though Ilford and Kodak give an ISO rating of 800 to 1000 for Delta 3200 and T-Max P3200 I'm happy to use them at EI 3200. In general the quality loss with pushed film is increased graininess, fogged up shadows and lack of shadow detail, as well as loss of dynamic range. But that's a generalisation. The usable speed of a film really depends on your tastes.
Both, but I don't bother with dr5 now. Scala processing is still available in the USA as far as I know. I send it to Main, and it comes back. The chemicals may not come from Agfa, but it is the Scala process rather than dr5.