I will believe it when the block size will be increased. Not before. I have absolutely no reasons to trust them.
Believe what? Their code is already out in the open. Are you even aware that the last functioning proposal for a Lightning network implementation was created by someone outside of Blockstream? No one's asking you to trust them.
I do not trust them to increase the block size, that is why it should be implemented by an alternative client. Unless the Core devs increase the blocksize, I will not trust them to do it. Especially since this has become a fundamental ideological disagreement, since not increasing the block size at all would lead to a very different future for Bitcoin compared to the future that restricting the block size would lead to.
Blockstream does not decide if changes are made to the Bitcoin core, the community of devs does.
I never said that Blockstream decides on changes within Bitcoin core. However you are missing a very important point. The core developers do decide what changes are made to the Bitcoin core implementation. However the core developers should not decide what goes into the Bitcoin protocol, this is a very important distinction, it is the economic majority that should and does ultimately decide on what the Bitcoin protocol should be, not the core developers. That is why it is so important that we have multiple implementations of the Bitcoin protocol, including multiple competing development teams. Decentralization of development should be a natural extension of the ethos of Bitcoin.