Thanks!)

1) He tried to span up this deal right from under my nose. No idea what "span up" is. He tried to steal this deal right under my nose. - he did it in front of me. That is, he was (figuratively) close to me. He tried to steal this deal from right under my nose. - he did it when the deal was almost mine, close to mine. That is "the deal was close" 2) He failed to get a rich prospective client, so his boss was dissatisfied with him. dissatisfied. 3) Her unusual perspective came in handy to us when we were deciding what is better to do. came is past, yet deciding is present. Better to chose one. "to us" redundant 4) My mother asked me to sweep the shelves before the guests come over. Ok, but I'd never "sweep shelves", dust the shelves? 5) He rubbed his eyes with disbelieve. Great 6) I had only vague understanding how the thing works. Ok, but much more likely to be "only a vague understanding". I have not even a vague understanding of 'span up a deal".

1) I don't understand "span up this deal" 2) That makes sense, but I think "dissatisfied" is a better term than "unsatisfied" (https://www.dailywritingtips.com/dissatisfied-unsatisfied/) 3) That makes sense, but "came in handy" is a little colloquial, and "to us" is redundant 4) I apologize because I am not 100% sure with this, but I think the right sentence would be "My mother asked me to sweep the shelves before the guests came over". 5) "disbelief" not "disbelieve"; the former is a noun, the latter is a verb 6) You need a preposition "of" or "on" -- "I had only vague understanding of how the thing works". Also, Russian has no articles, so another way you could write it in English with an article is "I had only a vague understanding on how the thing works"