Is it possible to read / find out information such as

• Speed
  
• Checkpoint times
  
• Distance driven
  

by a replay? I'm asking because this information is pretty difficult to achieve manually - especially distance and speed.

It's all possible.

Time to write a tool for that!

What would you use all that for in the first place? I can sort of understand checkpoint times, but the rest?

Well, as the thread name implies it's pretty trivial but I'd use them to check for top speed and average speed between two checkpoints (therefore time and distance as well). It would give me ideas for competitions on my maps at least.

I guess the information could also be used to check the flow of map sections, to compare the speed and split times between two ghosts, take the mean of multiple distances to a certain point in the map (taking screenshots during a race is a no-go ), to check the distance and time between checkpoints and so on. Just some ideas.

I could personally really use it to compare checkpoint times while hunting Nando maps or similar stuff. The reasons Voy mentioned also seem legit, so if it's not much work for you TGYoshi, you should go for it

Perhaps Lerya is exactly what you are looking for:
Race graphic viewer for TrackMania²

Well that tool comes in very handy if you're playing/practicing online on a server. There doesn't seem to be an offline-mode option though, where you can just throw in a replay and it gives you speed, checkpoint times, distance and other information - and that's what we're looking for.