Alpine skiing is downhill skiing, as opposed to Nordic or cross-country skiingWelcome to WordReference forums Tranzlator.
As far as I know a bowl in skiing terms is a bowl shaped valley or area (such as those called "cirques" in Europe, which are formed by glaciers), as opposed to straight ski slopes or long trails. I believe a technique called "bowl skiing" has developed to cope with this particular shape. It's a term fairly common in N America, as I understand it.
I think it would actually be unlikely to be suitable for children to practice; probably the reverse is true.
The word "Alpine" doesn't have any special meaning, I don't think. Resort skiing is sometimes called "Alpine skiing", from where this form of leisure originates.