Its certainly not slow. Have you seen the Churchill for example?
The kv-1 is quite quick given its durability and price point.
It'll 1v1 anything below a panther with ease, and even a panther it can be of use if supported.
Not quite. Economy wise, the KV-1 is no better than the Axis P4s (slightly better than OST, a bit worse than OKW, both cost-corrected) in tank on tank warfare if you compare a fight between KV-1/P4. I mean that would be alright, but it lacks in other compartments like mobility and AI as well as utility (P4s get at least Blitzkrieg and can doctrinally get smoke). Also, the KV-1 performs worse against high-armor tanks due to lower penetration, while P4s can "better" fight high armor vehicles.
So basically, the KV-1 is economically balanced if you use it to fight mediums. If you need it to do something else, buy something else.
More specifically to your post:
1. You can almost always find a slower tank. That does not mean the not so slow tank is "quick". The KV1 is neither slow nor quick, but lies somewhere in between mediums and real heavies, which is fine.
2. Tanks with similar durabilities (e.g. Pershing and Comet) are faster than the KV-1. Even Tiger is (a tiny bit) faster. Costs is not a good determinant for speed.
3. See the main post. Only true if you do not consider the costs of the respective units.