Hello, i've been looking around Lighting Network, and that seems to be a trusted third-party payment system. Doesn't that gonna against Bitcoin ideal?
No. Lighting Network requires no trust. If it did then people would just use online wallets instead or just old fashioned banks. It 100% relies on blockchain for it's security and is more complicated then that. You can read more about it here
https://bitcoinmagazine.com/articles/understanding-the-lightning-network-part-building-a-bidirectional-payment-channel-1464710791/It is pretty smart technology on it's own, people just assume that blockchain itself is as much as we can come up with and assume it is some kind of a known technology. It is new and different, not as big as blockchain itself of course, but it is still something different and very useful.
That was activated in Litecoin and doesn't seems that affected prices.
First of all, we use Bitcoin because it is useful. not for it's price. Secondly, Litecoin doesn't benefit as much from LN as Bitcoin, since it was already designed as a faster version of Bitcoin, but not as secure. LN allows for a possibility of secure 0-confirmation transactions (by bundling them together and then getting them confirmed).
Does Segwit have been Implemented to run Lighting Network, or it really have a big role in the Bitcoin Scalling?
No. Segwit is useful on it's own for multiple reasons. Bitcoin Core devs are really picky and careful, it wouldn't be a solution if it wasn't a clear non-compromising benefit. But obviously Lightning Network was considered, as it has clear benefits.