1. I think the grapple hook feels alright. It would be fun if it was a little faster and it felt more like you were swinging instead of just shooting straight towards the end of the hook. It was a little frustrating to have to actually click on the wall to grapple instead of the general direction of it. I kept trying to click in the middle of the volcano (in the direction that I wanted the grapple hook to shoot) instead of the wall. It might be helpful to have some kind of indicator to let the player know exactly where they can and can't click in order for the grapple hook to work. I think having a cooldown might feel frustrating since there isn't much the player can do to avoid the lava besides the grapple hook. Instead, I think obstacles should serve as a way of slowing the player down.
2. I think that you have a great foundation where a lot of different types of obstacles could work and make sense. The types of obstacles don't matter as much as the purpose they serve. Right now it feels like the only thing the player is doing is clicking to go up. Obstacles that force the player to be strategic and think about where they place their grapple hook would be good. Other obstacles that slow the player down might also be beneficial. It might be fun to have parts where the player can't grapple on to. Maybe it is foundationally weak and crumbles when the player tries (causing them to fall halfway up) or maybe they can't grapple there at all. Another thing to consider is having obstacles that slow the player down. Something that might be fun is having "cotton candy" or something sticky that if the player touches/grapples onto then they get stuck (or makes them move in slow-mo) for a short amount of time. Another obstacle might be hot milk bubbles that pop up from the bottom of the lava? I think having the lava pose more of a threat would be fun because right now it feels stagnant even though that is the biggest threat to the player.
4. I think the milk/lava is really slow as it is right now. This is mainly because the player can move so fast. It is easy to get really far ahead of it. So unless there are a lot of enemies/obstacles that will prevent the player from getting a huge start then it is a little slow even for the beginning of the game. If there were more obstacles that prevent the player from going up as quickly then I think it is at a good speed. Until you have the other obstacles in the game it is hard to know the right speed for the lava. Having random spurts in the velocity might be fun. Since it is going at a set speed it feels predictable. Increasing the speed later in the game would be nice.
Overall, great job! I am excited to see how the game turns out. I love the art and the overall theme/setting.