does someone has experience with playing Pokémon GO when you have used all FUP, so your connection was slowed? I am talking about 32kbps for downloading and 16kbps for uploading.
All games by Niantic (Pokemon GO and Ingress) are capable of supporting very low bandwidth connections without a problem. Ingress players have been known to play through BGAN terminals, which can be slower than Dial-Up at times.
Mapping data and Pokestop Image data will take a rather decent time to load, but they will be available for the rest of your game session. As long as you do not close the game or move into a new region, you will still be able to play. Note, however, that Pokemon spawns may take a very long time, and catch confirmations may take just as long.
Combined with current server instability, Pokemon GO on such a slow connection will definitely be possible, but may very well be an exercise in futility.
Yes, you will have a hard time downloading maps and images.
You will have to download Google Maps for your region as offline maps in order to have a chance to play. Circling your home area won't cause much traffic, but going further away might have an impact on your game as it keeps loading data (images from PokéStops, arenas, etc).
Edit: As mentioned below there is a chance the offline maps no longer work, but I haven't found a reliable source, yet. This would require kinda large downloads, if you leave your home area.