If the imam is fast, should I follow him or continue, for example, the tashahhud if he is quick?

No, we say you must follow the imam. The Prophet ﷺ said: The imam is appointed to be followed. When he says takbir, you say takbir. When he bows, you bow.

So he must follow him, even if he misses something obligatory. Even if he misses something obligatory, following the imam in that is more important. And Allah knows best.