I tried to apply a similar scenario to Bitcoin mining. We all know that several miners around the world compete to solve a difficult mathematical problem, which aids the creation of a block. After the successful creation of a block, the miner is rewarded with some Bitcoin. Sadly, I can't tell the exact number of miners globally, but I think their population is enough to make the reward process very tough.
Yeah, you've started the wrong way on almost every single aspect of it!
Miners are not taking turns at finding blocks, the number of miners is meaningless, it's the hashrate they control, the reward process is not "tough" is just math on splitting the reward, just like it's economics in running a mining business!
So your questions are just 101% wrongly worded, there is no asnwerign them!
Now as a solo miner, you need to have a hashpower to be able to counter the combined hashpower of the all the miners in the world to be able to generate enough coins to either ROI and break-even or profit beyond break even point.
Actually this is not true as it's not really a hashrate competition but how much that hashrate costs.
You stared well but got sidetracked, if of course we're not talking about usb sticks , a miner who buys his gear cheap, is paying 1 cent per kwh and he runs his own farm alone will manage even with solo mining to out profit in the long term any other miner or even mining company even if he has a few hundred of petahashes not exahash.
He will only get a block once a month but long term as randomness starts giving away his lower costs will have the final word and he will be more profitable even with 1/100of the hashrate!