[SalesForce] What are the available $A JavaScript functions in Lightning

My experience has been that you would use the custom attribute approach if you wanted to expose the value to be set externally by the container (an app, another component, etc.) of your component. One benefit of that would be that the container could "share" the value across multiple contained components if need be like in this question. You can also do fun things like set the value through an URL parameter.

The value attribute that you can get from the ui:inputText (v.value) is itself an attribute of the abstract ui:input component and already exists to hold the value, so if you have no need to expose it as part of the component's shape / API, then you shouldn't.

Bonus Answer

I have no insight into the roadmap or anything like that (maybe someone from Salesforce will answer), but I tweeted the same general question about LDS, the sldsx components, and the ui:inputs. You can see it in this conversation, but the telling part to me is that the Salesforce1 Style Guide that used to thoroughly list all of the Salesforce1 styles with an URL of http://sfdc-styleguide.herokuapp.com now redirects to https://www.lightningdesignsystem.com/ .

You can use most of the standard JavaScript functions. There are a few that are not implemented for security reasons. You can see what's available and what's not in the Locker Service API. Several notable examples of things you can't use include ServiceWorker, ShadowRoot, MutationObserver, and a few others. For the day-to-day features that we typically use, like Array, Math, and Date, you'll find that all of those are available as usual.