Think about 100m race. if you put Usain Bolt against 100,000 one legged dwarfs then there is still going to be only one winner.
Now I might be completely wrong as I have not read up on how the actually mining and network for crypto coins work but I am sure as hell that it does not share the work equally between all cpu's in a botnet to find the solution quicker.
No. Think of it as a lottery. Miners will try to guess the correct number. You can buy 5 tickets with your 5GHz cpu, and 1 ticket with a 1 GHz cpu. 5 tickets will win far less than 100 tickets.
Same thing as I said but different analogy. My whole point is botnets are seriously not an issue.
In fact its not as simple as that. Each new block starts a new sequence of calculations. Its not just a case of picking a random number and hoping. Its running an algorithm trying to find a result. The i7 has a much better chance because it can handle far more clock cycles than something like a 1ghz cpu so i7 will always have a far better chance.