Can you play any dynamics and tempos of any kind or do some not go with the others? For example, can I play fortissimo lento or an it only work if I play presto or around that speed. I am only talking about extremes here. I am not sure playing presto in pianissimo can musically work?
The two aren't related in any other way than they both tell of different ways to play. Tempo is obviously just the speed, while dynamics/articulation are about the way something is played, the volume, the attack, the length of notes, how they mingle with each other, or not.
So, something could be played legato and loud, legato and quiet, or staccato and loud, staccato and quiet, with all stops in between.
Some combinations are easy, others not so. Loud and slow is probably easy, as there's time to lift hands for the next thump. Staccato and fff will need some working on.
If you're asking whether you can change the written dynamics/tempo/etc, then yes, of course. It may be beneficial to the piece, or may degrade it, but it's rather subjective.