It's not possible for a peer to steal funds. Your funds only move from one node to the other when routing payments. You incur a small fee for opening/closing channels, and there is the possibility of force-closing a channel causing a somewhat higher fee from yourself or your peer, but typically is not very much. Experienced, well managed nodes would have this happen less (in my experience) but occasionally it still happens.

The protocol for opening dual-funded channel is similar to you signing a transaction when you spend a utxo. The tx is verifiable on the btc base-layer. That is all.