Can iBeacon range/region monitoring trigger "dynamic"/data-based notification? Can an iBeacon range and/or region event (for an iOS app that is not running in the foreground) somehow have a "dynamic" notification send to that iOS device (i.e. a notification text that is not hard coded in the app but rather comes from a server)?

An example use case that everyone can relate to is that your local super market implements beacons and that as you walk pass the milk section you get a notification saying "Milk half price for the next half hour" (because the "use-by" date is near).

I know I can do local notification with static text (i.e. "welcome to the store") but unsure if I can so something more dynamic.
Yes, beacons with their proximity detection capabilities can directly push content in the form of notifications to the lock screen, thus allowing consumers to interact with apps without having to open one.

You can use features like cards, rules, webhooks for creating such notifications.


With Cards (Cards are small pieces of content - text, photo, video or audio - that are
to be shown based on the campaign rules), you can edit the kind of content you would want on the screen as a notification. 
Rules allow you to define a set of conditions that must be satisfied in the proximity of a beacon, for actions to be performed inside the app. 
Webhooks are "user defined HTTP, URI callbacks". They are usually triggered by some event and when that event occurs, the source app makes an http request to the uri configured for the webhook.


Probably the dynamic variable you are referring to here is the RSSI value of the beacon frequency which increases when you reach a beacon. Couple that with UUID-Major-Minor and you can do custom data based notifications.

You can also use various SDKs that have already incorporated these features, through something called camp-on's on a beacon and cannot only do local notifications but also call webhooks among other things, as a reference on Github. 
If you are interested in learning more about how to go about building a beacon-enabled app right from scratch,  join the Online iBeacon App Development Course: Build a Beacon-enabled iOS App. It will help gain insights on location-based services and also understand terminologies like beacon ranging, background monitoring and much more.