Could someone theoretically set up a node to siphon seeds from people who connect to it? Or is the seed always safe? How is it handled internally?
No, a node cannot steal your seed
When you send a transaction to the node you are connected to, you don't send the seed to it. The tx (=transaction) gets created locally on your PC/Smartphone/other device and it also gets digitally signed with the seed*.
So it doesn't matter if you trust the node you are connected to or not. The only thing that could happen if you are connected to a "bad" node is that your tx doesn't actually get published because the node doesn't forward it to it's neighbours.
*with a private key created from the seed
The seed is required to generate a private key. The private key is used to sign the transaction. All of this can be done offline.
Finally you send the signed transaction to the node and the node broadcast it the the network. A wallet (except a malicious one) will never send your seed over the network.