Can I create a new account in Ethereum (with MIX IDE) by calling a contract method triggered by a button event in the html/js Dapp ?
I don't think smart contracts can do that. EVM on which smart contracts can run has the following limitation
The Ethereum Virtual Machine or EVM is the runtime environment for smart contracts in Ethereum. It is not only sandboxed but actually completely isolated, which means that code running inside the EVM has no access to network, filesystem or other processes. Smart contracts even have limited access to other smart contracts.
So instead you can do json-rpc and use the personal object from web3 to do so. For example web3.personal.newAccount(""); by including web3.js in your browser.However this approach may not be the best option as mentioned How can I make new account by JSON-RPC?