Why are there no Sarmatian invasions during EB's period?

[Jolt]

Can't they grow anything in those places? Like teas in some mountainous regions in China?? I'd be surprised if there is any land on earth that can grow grass but nothing else.

Growing? Yes, they can, with sufficient labour and hardwork, grow many things in hostile soils (Bad weather, rocky soil, having to dig deep and keep revolving the lands). But as I said, it takes too much time and labour, without sufficient guarantees of a successful harvest, how small it may be, if one at all. But I do recall asking for an example. Tea wasn't grown in Europe, nor was in Persia at those times. Furthermore, tea wasn't very valued in the Chinese society at the time of the game, thus was not a lucrative product, and thus wouldn't spread through commercial trade.
EDIT: As for your very first question. Lusitanians, for instance did use mountainous oaks to collect acorn. They in turn used these to make acorn bread. But they didn't grow them as far as I'm aware.

Like Romans, of course :)

Alexander payed for nomads in his campaign in Bactria. Did the Macedonians citizens suddenly began feeling their economic power diminished? Did they suddenly began getting greatly overtaxed? How many even knew that he hired nomads?

It's the same thing. As I wrote in previous post, anyone in a socity who is not doing productive works represents a cost to this entire socity.

You could argue that they wouldn't do anything else, well then why not just remove them and replace the army of nobles with levy or professional soldiers?

Did the Macedonian economy cripple down because many Macedonian noblemen left Macedonia with Alexander when he went to fight the Achaemenids? Nope. Things aren't as interconnected as in the modern world, mate.

Because levy or professional soldiers (Or 99% of them, at least. Those who would be rich to afford such things wouldn't certainly be risking their lives for someone else) can't afford good quality mount, heavy armor (Both man and horse), weapons (spear, sword, bow, quiver, arrows), shield, etc. Btw, what do you mean by professional soldiers? Mercenaries? If so, then read the first parentesis of this paragraph. The professional soldiers are the noblemen.