It can be extremely difficult to determine the start of a language. When would one consider the beginning of English? Modern English is a blend of Celtic, old German, old French, Old English, all sorts - so would you consider the start of “English” as being before the Saxon invasion, before “German” was introduced and a sort of Celtic was spoken? Or would you consider it to be more towards Shakespearean times, when language started becoming more like what we consider “modern English”? The question of when languages “start” is incredibly complicated because they go through so much change.

As for when they end, I’d say to look at Latin, frankly, as it’s the most obvious case of a dead language we know. After the fall of the Roman Empire, it divided into many different dialects. It was a clear case of an empire falling and thus its spoken language ceasing to exist. Obviously there are other reasons why a language may end - Welsh and Catalonian suffered due to the rule other nations had over them, and they could have easily died if they weren’t revived. Populations may die out, other languages may become more prevalent in the nations they’re spoken, or a language could be seen as having “ended” because it has evolved into a very different language, e.g. Old English to what we speak today.