1) how do they process transaction so quick
If certain conditions are met, it is VERY difficult to keep a transaction from being confirmed. Risk can be reduced to an acceptable level by monitoring the bitcoin network and watching for high risk situations.
- afaik it is possible to cancel it before firsr confirmation?
Have you ever even tried sending or receiving a bitcoin transaction?
There isn't any reliable method to "cancel" a transaction. Most transactions that meet some simple conditions will confirm no matter what you do to try to "cancel" it.
I was told that first cinfirmation takes up to ten minutes.
You were told incorrectly.
A blocks will be solved "on average" every 10 minutes. Under some circumstances it can be very likely that a transaction will be confirmed in the next block. That can sometimes happen within a few seconds. Under some circumstances it can take over an hours. If the transaction doesn't meet certain conditions, it may not be included in the next block and then could take hours or even days. There are steps the sender can take to increase the likelihood that the transaction will be confirmed in the next block.
2) how does processing center gets notified about transaction?
That depends on the processing center, but I would expect most processing centers to monitor the bitcoin network and watch for transactions and blocks.
Bitcoind has hooks and is able to notify other software that payment is commited or they use some kind of longpolling, or mayb it's a home-rolled solution?
I would expect the best processing businesses to create their own node for monitoring the bitcoin network.