I agree with Zanipolo that the whole "Celtic" thing is very unsettling if you start digging. The problem is that a lot of our research is based on classical texts, that can be quite vague to translate and prone to exaggeration and clichés. To answer to LD's question to the best of my limited knowledge, I would say that Gaul was celtic before Cesar's invasion and shortly afterwards. As for how long it had been celtic at that point is probably never be known, but it is safe to say that Celts coming from the east settled and mixed with locals, and might not be seen as "true Celts" anymore. I recommend you check Barry Cunliffe's books, they are pretty accurate, as are Wencelas Kruta's works. The problem with Celtic studies is that some pseudo-scholars wrote a lot of garbage (the worst of them being French writer Jean Markale) that totally discredited serious academic research. I'd be delighted if you'd share your reasearch with us at a later stage. Good luck...
I agree in so far as that the problem, indeed, one of the main problems is that there is not "one" definition of who or what a "Celt" is, and that several definitions are around which are sometimes used in free variation with each other (partially because there is also significant overlap between them):
1) in the historic context, the "Celts" were the people(s) that the Greeks refered to as "Keltoi" or "Galatoi", and the Romans refered to as "Celtae" or "Galli". What might be added is that the term "Celt" appears to have been an endonym (self-designation) of the people that inhabited that the Romans perceived as "Gaul" and the lands along the Danube.
2) in the archaeological context, we associate the culture of La-Tene with the people described in #1. We thus might (with a big caveat) describe it as "Celtic".
3) in the context of linguistics, anybody who speaks a Celtic language. This is actually a very clean-cut definition, but when looking into ancient sources, this poses a huge problem since the Celtic-speaking peoples were for the greater part illiterate. This means, the main source of information about them are onomastics, that is place names, personal names, deity names, etc. - all these sources are only basically from the Roman period, and it's admittedly a gamble to try to project this on the situation centuries earlier.
(if we compare definitions #1, #2 and #3 against each other, we notice a striking difference: although linguistically clearly Celtic, the Romans never refered to the Britons or the Gaels as "Celts", and the term is only used inconsistently to the Celtic-speaking peoples of the Iberian peninsula. Likewise, the La-Tene Culture certainly didn't encompass all Celtic-speaking peoples - and conversely, people like the Illyrians and Thracians adopted La-Tene styles without themselves speaking a Celtic language)
4) a denizen of any one of the modern "Celtic" nations, regardless of wether they speak a Celtic language or not (after all, with exception of Welsh, they are all either endangered or moribund). Since there never was a unifying "Celtic" identity until modern times (read: neither the Gaels nor the Britons refered to, or saw themselves as Celts until ca. the 19th century), it's obvious that this is a modern construct and when erroneously applied, can lead to a lot of confusions (which is why I think it's the worst confusion).
One problem that I see with the whole discussion with anything "Celtic", whenever it arises, is that I think people are almost always biases in one way or another, especially in the way that they have become a subject of a strange kind of romanticism (or worse, nationalist/irredentist agendas) that is projected onto the past, and my sad impression is that even many scholars have succumbed to this. A truly bad very recent example in popular culture would be Pixar's "Brave" film.
