1) Anyway how come the "I-buy-bitcoin-from-a-dealer" price at localbitcoins is sometimes LOWER than the "I-sell-bicoin-to-a-person"? BTW usually the bitcoin buyers have better reputation than the low-price bitcoin-sellers, but assuming it isn't a sort of scam. You could have money instantly without an effort, or couldn't you?
There are several possible reasons. The possible reason is false advertising. I'm aware of someone that lists a price on localbitcoins that they don't intend to honor. Then once you've established a contact with them, they will alter the amount of payment they require.
2) BUT when you buy 1 bitcoin from some seller (perhaps not localbitcoins, it may be another "service"), you spent some money, which can have a long road ahead and meanwhile the price of bitcoin goes higher, does the seller send you 1 bitcoin or less? (and when the price lowers he could give you more than 1 bitcoin
?).
Depends on the person and the terms of the deal that you work out. For face-to-face exchanges, I always give the customer the option of either locking in the exchange rate, or letting it float until we meet.
3) What defines volume of you bitcoin wallet? Transactions stored on every bitcoin-qt equipped computer or what?
I don't understand the question? Your wallet should display a quantity of bitcoin that you control with that wallet. That quantity is determined by the unspent outputs that the wallet has the private key for.
No, the Bitcoin-Qt wallet does not do this yet.
the old blocks are somehow "cropped" that they have smaller size
That would be the plan.
and bitcoin clients have some ?checkpoints?.
Checkpoints already exist.
a non economist question:
4) Where does the Bitcoin value come from? Somebody (Satoshi) has just invented a currency and now there are "redundant" billions of i.g. dollars?
The value comes from the interaction of supply and demand. There is a limited supply of bitcoin. People desire bitcoin (demand). Therefore, they are willing to exchange something of value for the bitcoins.
