If they are using the standard protocol then how do they connect to the Ethereum network? Do they use their servers as proxy to the network? Because if it's so, that would defeat the whole point to me.
No, they're not using the Light Client yet for that very reason, but easily could in the future. But in any case, no crypto wallets are light clients. All Bitcoin wallets, for example, use servers because it's impossible to do Bitcoin light clients (at least, they haven't found a solution yet).
This app is more about having WeChat with crypto payments and with app interactions. Light client could come later though.
It verifies enough information to be secure. It is obvious that at one point they need to connect to some node because this ia the way blockcgain works.
That doesn't exist per definition. You cannot have a light client that its own node and it is not the node defined in the specific blockchain. The bitcoin innovation was about using a common ledger for every node and the nodes must run specific code to check that the blockchain state is the correct one.
If you find a way a node can do less work that what is doing now without relying on another node you would discover something new at the computer science level, so this light node will transform into the definition of a node.
So for now the Ethereum promise to have a distributed network where I don't need to trust any man in the middle is really not possible yet on mobile devices?
In theory, you could run a private client on DigitalOcean and then connect to that. Apart from that, true light clients are coming [1].
Particularly interesting is this comment by the ethereum light client developer: [2]
"Can't promise anything yet but we're not that far from real trustless O(1) light client syncing."
If they are using the standard protocol then how do they connect to the Ethereum network? Do they use their servers as proxy to the network? Because if it's so, that would defeat the whole point to me.