How can clients ask new requests on Asana ?

Many use forms yes, others give agencies access directly to the project. Depends on your preferred way. In the first response I shared a link to a post with different ways of dealing with clients.

You will be able to share the link to the form or you can also embed it on a website. And yes sure you can also create a task where you add the Asana form link.

You can create this via rules.

Best to check your notification settings in the project then: https://help.asana.com/hc/en-us/articles/14249899700379-Email-notifications

Otherwise what you can do as well is trigger a comment via a rule.