I can't tell you how it works in A. On the invoxia website there is a link to the different providers for the low power networks. When you register the tracker, you have to say in which country you want to use the tracker. If you choose Switzerland, the tracker will run on the Swisscom network. In my experience, the coverage works great there. But only in Switzerland. If you select Germany when setting up, the tracker will work in the Sigfox network. Then it should also work in A. However, I didn't really understand the Sigfox coverage map, how good/dense the coverage really is. I live near Basel. It's not much use if my döffli is stolen and disappears abroad after 7km as the crow flies. Sigfox also works in Switzerland. But the network coverage is not at all comparable with the Swisscom network. Accordingly, I receive much less location feedback from the tracker.
These trackers are also available with 4g instead of lowpower according to the invoxia website. Whether that would be more suitable because of roaming$ etc. I don't know.

Not sure ... but I see no reason why not. GPS signal is the same