If you mine on p2pool you can increase your earnings significantly by joining the bonus hashrate raffle @ https://xmrvsbeast.com/

If someone is new to mining and has no idea what is going on they can use this GUI mining kit to get started https://github.com/Cyrix126/gupaxx

But mining is sooooo fun!!! ⛏️ Especially with p2pool and https://xmrvsbeast.com

Yes, they are statistically sound I believe. The source on how the calculation is performed is published so you can review the formula being used.

If you think there is an error do let me know and I will evaluate.

There is a vanity address generator software. You let it run for a long time and it will find some.