Well... given than mitochondria eve was around 99–148 thousand years ago https://en.wikipedia.org/wiki/Mitochondrial_Eve The human species is at least that old.
So a human baby from 148 000 years ago likely could learn to do all the things listed.
Could Neanderthal do all those things... Well Neanderthal are not an ancestor species.. more like a cousin species (separation by 500,000-700,000). And from hyoid bone... appears to be able to speak like modern humans do.
So probably yes.. on mastering modern language.
Reading and writing.. well no idea. But then again there are no examples of humans writing older than 3200BC. And the human species is at least 150 000 year old.
However Neanderthals do have a reduced semicircular canals compared to humans. An almost defining feature of Neanderthals.... so Neanderthal were probably less graceful in 3d space... so probably no gymnastic and kungfu for neanderthal.
Homo erectus... well they have high larynx.. limiting the sounds the they could make. The position is approximate that of a human 2 year old.
The other things on your list... no answer can be given.