How do I write parallel and/or concurrent apps for Flutter?

Flutter supports isolates. Isolates are separate heaps in
Flutter’s VM, and they are able to run in parallel
(usually implemented as separate threads). Isolates
communicate by sending and receiving asynchronous messages.

Check out an example of using isolates with Flutter.

Can I run Dart code in the background of an Flutter app?

Yes, you can run Dart code in a background process on both
iOS and Android  For more information, see the free Medium article
Executing Dart in the Background with Flutter Plugins and Geofencing.

Can I use JSON/XML/protobuffers, etc. with Flutter?

Absolutely. There are libraries on
pub.dev for JSON, XML, protobufs,
and many other utilities and formats.

For a detailed writeup on using JSON with Flutter,
check out the JSON tutorial.