Use agar as a coagulant to make homemade tofu

Well, that's basically where ice machines come into the game. Often ice recipes tell you to stir the ice during the freezing process every 5 to 10 minutes or so, so the ice will stay softer. That's what ice machines are taking care of: While freezing the ice they constantly stir the mass, so in the end you will get the perfect soft ice. Anyway if you then place this ice in the freezer, it will become hard nevertheless, since finally it's all a question of temperature.

So you might either go invest in an ice machine or get the ice out of the freezer (and into the fridge) some 15 to 30 minutes before serving it.

There's definitely no other way around it.

Agar is not a good choice for pudding because it makes a brittle gel and it won't melt in your mouth at body temperature. What you want for pudding is a starch based thickener. What we call pudding in the US at least is typically thickened with cornstarch. Modified starches like Ultra-Tex 3 can also work well. Are you thinking of something more along the lines of panna cotta, which does normally have gelatin in it? If so, you might try carageenan instead of agar. Here's a recipe that looks promising: http://irishherault.wordpress.com/2009/12/24/vegetarian-panna-cotta/