Did I calculate maximum price of machine correctly?
The thing you are missing in your calculation is that the roubles the machine produces in year 1 are more valuable than those in year 2.  Think about 2 different machines with different production schedules


Machine 1 - 440 roubles year 1, 0 in year 2
Machine 2 - 0 in year 1, 440 in year 2


Using your calculation the value of both of those machines would be the same about 306 roubles, but machine 1 produces the goods in year 1.  So in year 2 you can put those roubles in the bank and earn 20 percent interest on them.  So at the end of 2 years you actually have 528 roubles instead of 440.  

What the NPV calculator is doing is taking into account the production in year 1 is worth more than the production in year 2 by dividing it by a smaller number, $(1+0.2)$ instead of $(1+0.2)^2$.

Regarding the part about $i$ meaning different things.  $i$ is how we tell how muc we value a dollar today relative to tomorrow.  In the real world inflation makes things in the future cost more so we discount future dollars by that amount.  In your problem a dollar I save today is worth 1.20 tomorrow so if I invest that money in a machine I better earn at least that much otherwise I'd rather put it in the bank.

Explanation of NPV:
Think of there being 2 different machines.  One gets you 240 in one year.  The second gives you nothing in the first year but 200 in the second.  Using your calculations you would say you'd pay 
$$ \frac{240}{(1+0.2)} = 200 $$ 
for machine 1 and 
$$ \frac{200}{(1+0.2)^2} \sim 138.9 $$
for machine 2.  Thus you better be willing to pay 338.9 for a machine that does the work of machine 1 and machine 2. That is all NPV is doing here.