Taking your questions in order:

How yet another "currency" will solve anything, or what Bitcoin is supposed to be solving?

Because this is a currency that has different properties that avoid the properties of other currencies that create these problems. For example, the supply of Bitcoins is fairly precisely defined and nobody can devalue them through direct supply inflation. Nobody can discover an asteroid full of Bitcoins and increase their supply.

How computers are creating currency that I'm supposed to trade my labour(or fruits of) to a human being who somehow claims ownership of this currency?

It's the same way other decentralized currencies work. If you use, for example, gold as a currency, someone goes to the effort of mining the gold. Then they trade that gold for other goods and services they need to continue mining. Others trade goods and services for the mined gold. With Bitcoin, computation work is needed to secure the transactions, miners get newly-created currency in exchange for this service. You have to distribute a decentralized currency somehow.

How to become the owner of such currency?

Buy it on the open market. There are many sites where you can buy Bitcoins. You can't really mine Bitcoins at a profit easily -- if you could, then the number of miners will increase and they'll each get smaller shares. This will tend to keep mining just barely profitable, for those who do it well, over the long term.

How the value of this currency is determined, if it came from nothing?

The same way as the value for anything else is determined, supply and demand. It's value is whatever price buyers and sellers meet at.