Thing is, it's difficult to consider Celts as a really well-defined ensemble historically : while in the ancient sense, it mostly was about Gauls or part of Gauls; it took a wider meaning since the XVIIIth century to name peoples related by language then retroactively applied to peoples sharing similar material cultural features from the British Isles to Anatolia.

Rather than "Celts" ruling over most of Europe, however, most archeological or historical specialist favor the idea of various indigenous cultures more or less related by language (where it can be attested, which for Central or Eastern Europe is difficult) and material cultures associated with historical Celts (especially Halstattian or LaTenian archeological horizons during the Iron Age).
The problem is that both don't always overlaps : insular Celts were at the periphery or even outside both of the cultures associated with Celtic Iron Age in the mainland, Hispano-Celtic cultures were outside La Tenian horizon while part of Halstatt, etc. Likewise, it's probable that the LaTenian elements found in Easter Europe weren't carried over by Celtic-speaking populations, at least not entirely so.

I'd advise you to look at the answers in "What's the problem with the word Celtic", especially from u/PurrPrinThom or u/Depanneur, and to look at an earlier answer

In a sense, your last question is unanswerable : the difference we set between "Celts" as an ensemble of related people and other peoples is mostly an historiographical term that would have been confusing for ancient authors for whom a "Celt" was first someone from Gaul, although neighbor peoples would have been diversely related to.
Does that means that there was no Celtic ensemble? Of course not, but as a "meta-cultural" space with various branches evolving more or less separately on their own social, economical and political grounds : for example; the Gaulish touta and the Irish tuath, while linguistically and socially related seems to define different institutional realities.

The relative obscurity when it comes to the intermingling of Celtic and non-Celtic elements (not even mentioning the mix of various Celtic elements, as it was probably the case in Northern Italy or southern Britain) makes it difficult to really address the nature of the relation between various communities : we're, however, probably looking at mutually acculturating communities in Germania, Eastern Europe and Anatolia Celtic-speaking peoples seems to have mixed with non or para-Celtic groups fairly commonly and without clear boundary.

For example, tough the distinction between Gaulish and Germanic people might came from pre-Roman geopolitical conceptions, the distinction between Gallic and Germanic was mostly about geographical and political realities; the Roman conquest later essentializing the differences between both (especially as Germanic-speaking groups came to dominate southern Germania as well in the Ist century BCE) as being wholly different.

Depending on the historical and geographical context of these ancient peoples, of course, the situations were different : the idea is that a great deal of the make-up of Gallic, Germanic, Balkanic peoples associated with ancient Celts was made on an indigenous and mutual (if asymmetrical) acculturation.