How is this machine used? (for, I think, peeling the skin from the tomatoes)

Generally, there is no reason not to use it. However, I'm hard pressed to think of a good place, generally because good cooking prefers other, stronger flavored liquids instead of water.

An application where you can have the flavor on its own would be making ayran or a lassi. I think it would be an improvement over plain-water-ayran.

For other uses, just substitute plain water to get a slight nutty hint. I like to pair rice with nuts, so you could use it instead of pure water to cook rice. Or add it to a pot of stock you are making - with a complex stock of a meat and several vegetables, it will be too subtle a taste to register consciously, but will enrich the flavor as a whole. For a simpler stock (e.g. just chicken with classic mirepoix) the taste of almonds can get too strong, depending on the quantity you use.

I would say it's totally up to you.

I prefer it with the skin still on, it get's really juicy inside. However it's a bit more difficult to eat. So perhaps if you were making it for kids (although, you could just skin them after they are fried), you could skin it.

One opportunity I really think is better without skin is when you serve it with sauce. Having to fiddle around with the skin covered in sauce is not really handy nor fun.