Is there any possible theoretic way to alter the blockchain of bitcoin?
Only of you get enough Nodes to agree with your alteration. F.E. if you have more Calculation Power as the combined rest of the Network and the alteration doesn't violate any protocol rules.
Or is it possible to create an own address where you can choose your own characters?
Adresses are created out of your private keys and there is no way to know how it will look before.
But you can create vanity addresses simply by trying often enough, there are programs for this like vantigen (see the Address in my sig.).
But the time needed grows exponentially with each additional character.
Is it also possible to send unconfirmed bitcoins?
Yes, this is indeed possible, not with the standard client, though.
And any unconfirmed coins you send, will of course not confirm before the Transaction that you received the coins with has confirmed.