"The risks of this business are high!"
Translation:Riscurile acestei afaceri sunt mari!
Correct solution: Riscurile afacerii ăsteie sunt mari! Isn't 'ăsteie' supposed to be 'ăsteia'??
And, if 'asteia' would also be correct (I dont know, wikipedia says it is the same thing?) when would you use 'ăsteia' and when 'asteia'?
That's indeed a mistake, it should be "ăsteia".
As for your second question, there isn't any semantic difference between the two forms, they're just variations. I'm not sure, but maybe they vary by region; the vast majority of people I know (including me) use "ăsteia".
"Ăsteie" is indeed incorrect. "Ăsteia" is the correct form. "Asteia" is not often used and it sounds weird. However, I wouldn't use "Ăsteia" it is informal and is only used in some parts of the country. "Acesteia" is the formal and polite form. (Trust me, I am a native speaker)
I disagree with the view that longer forms are formal and shorter ones are informal. I'd say most of the long forms of the demonstrative pronoun sound awkward and I hardly hear people using them.