1.) I think the grappling hook does have a very high amount of force, but I don't see that as much of a bad thing. I think with lower force a lot of obstacles would be much more annoying to navigate, so I think I'd keep it as is. The only real downside to having it be so fast is that you can outrun the milk lava very quickly.
2.) I think enemies/spikes that you have to avoid would help keep players from just spamming the grappling hook, but I also don't think that enemies would fit in such a small space as you have for the volcano. Honestly I don't think you could add any obstacles at the moment, it would be too frustrating. If you scaled down the player to about half size I think then it would feel fair (or scaled up the level sections to double size).
3.) I don't think I saw the milk lava the entire game. Even when I finally decided to jump down and see how far I'd come my velocity was fast enough that I didn't even see the milk before the game over. So I guess that probably answers your question, I'd say too slow.
One other thing that you didn't ask about- I'd very much consider decreasing the size of the character. The one level section where you have to squeeze through a small gap is more frustrating than anything because it feels random if you can even get in or not. I imagine the frustration would be multiplied many times over if I was on a time limit because of the milk and I couldn't get through the section.
Also, I'm not sure what the purpose of the walking and jumping is. I never used it, except for one time when I clipped into a wall and I walked out of it to get back into the level.