And in the usages of 1.1.1.1, no one was publishing anything on BGP or pushing it out to global routing tables. However, they were building their own infrastructure (and, in the case of consumer routers, their customers' infrastructure) on the assumption that this portion of the namespace would never refer to an external resource they'd actually want to access.
Similarly, if you use .ars, you're taking up that namespace from the perspective of your internal users. If at some point it turns out that there is some resource under that name that you want to access, you're going to have a hell of a time rebuilding your infrastructure to not use that name.
tl;dr don't use random names in a globally-managed namespace. Even if you're the only person seeing those name -> resource mappings, you can end up with inconsistencies between your own usage and the globally-managed version.
No, you're not, because an internal management network does not have a gateway out to the internet. The management VRF does not talk to the global routing table. There would be no way to access a public .ars website even if you did not take its namespace.
With a totally internal DNS setup it doesn't matter even if ICANN does decide to create a ".ars" TLD someday. In such a theoretical setup, your clients are all querying your own internal DNS servers, and you are not publishing or pushing anything to the root nameservers. Your use of internal hostnames and rDNS for ".ars" internally does not conflict with or hurt anybody's use of their own domains in the real-world .ars out on the public Internet, and neither does their use of the domain affect your non-internet-connected management network. There is no "stepping over other domains".