Although I don't see gyroscope support in the standard list (here), there do seem to be multiple Cordova plugins for it: here and here.
Absolutely. This is achieved in two steps:
If we take Geolocation for example, here's an existing widget in the App Store that provides the function of returning latitude and longitude to an object and calling a microflow. This widget uses the Cordova GeoLocation plugin to retrieve the lat and lon. If you look at the docs for that plugin, it can also provide heading, speed, and altitude as well:
position.coords.heading position.coords.speed position.coords.altitude
Making these properties available to your Mendix app would involve simply adjusting the custom widget to read those values as well.
Here are links to the plugins for the gyroscope and accelerometer as well.
If you need help building these widgets, Mendix Expert Services can help you, as can a number of our partners and community members. Good luck!