You'll need a database to keep track of the user's addresses and the Bitcoins in each of the addresses. Ensuring the security and managing the Bitcoins for users is no easy feat and it generally isn't recommended for anyone to develop wallets from scratch.
To craft a transaction, you don't need a full node or any client for that matter. All you need is to write a code which manages the scripts and signs the transaction using the private key. It isn't very hard and there are quite a few libraries[1] that you can use.
DNS seeds fetches the IP addresses of a few nodes that are always online on the Bitcoin network. The seeds are not nodes by themselves and you cannot request any usable information about Bitcoin blockchain from there. You can only query and send information over to the Bitcoin node but you can't connect to them to create transactions.

I won't recommend you to only retrieve information without further verification. Operating a payment server without operating a full node is dangerous given the attack vectors.
[1] https://github.com/1200wd/bitcoinlib