Yes! ~800kya is a common estimate.
Strong differences: it's not so clear these are "strong", for a couple reasons:
1. The archaeological record has disputed some of those claims: spears are supposed to have been part of the hunting repertoire of Neanderthals [1], there are some claims regarding musical instruments (personally I'm skeptical) [3], and cave paintings [2] basically resemble what sapiens where doing about that time, which is just... not very impressive in general.
2- A much more interesting question is hiding in plain sight. It's not as much "did Neanderthals do X or Y relative to what sapiens are known to be capable of?", but rather: "given enough time, could Neanderthals or Denisovans have painted something like the Lascaux cave paintings?". Or, rather: did all these extinct humans species have the same capability for cultural ratcheting, ie transmitting and refining knowledge, that we have proven to have? Sapiens needed a lot of time to create some of our most representative "representative art", let alone other cultural innovations. On the other hand, if there were any differences in capability, what were their nature? What are the implications for language?
Re the basis: for sure! Some of the innate physical and neurological basis for language have been in place for a long time. Which pieces where co-opted, modified or appeared de novo when and for what is the interesting part. Having only the archaeological record and the DNA of these species, it's a hell of a problem.
As for the shrinking brain size: as far as I know there is some doubt about the universality or significance of this claim. It could be due to agricultural diet changes, or holocene climate fluctuations. It also coincides with population size increases, so mutations allowing more efficient brains or just regular old drift are possible. Honestly, I can't say I have a strong opinion on it.
[1] https://www.nature.com/articles/s41598-018-37904-w
[2] https://www.science.org/doi/10.1126/science.aap7778
[3] https://en.wikipedia.org/wiki/Divje_Babe_flute